carry in carry 1101 carry carry

Size: px
Start display at page:

Download "carry in carry 1101 carry carry"

Transcription

1 Chapter Binary arithmetic Arithmetic is the process of applying a mathematical operator (such as negation or addition) to one or more operands (the values being operated upon). Binary arithmetic works exactly like arithmetic, except that 2 (not ) governs how individual digits are interpreted and manipulated.. Addition To add a augend a and addend b, the sum s is constructed by adding digits one at a time from least to most significant digit. If in any position the result is 2,ais carried into the next more-significant position [Alg..]. 5 8 sum out in A non-zero out of the most significant digit indicates unsigned overflow; the result is larger than the largest value that can be represented (2 N, for N bits) out in sum Two s complement signed addition is the same as unsigned addition (because 2 N the additive inverse of x, modulo 2 N [Sec. 2..4]). x is -5-2 sum in out to msb of msb in sum in out to msb of msb in If the signed result cannot be represented in the number of bits available then signed overflow will occur. Signed overflow is indicated by the in to the msb being different to the out of the msb. 9

2 Algorithm. Binary addition input: N-bit augend a and addend b, and a -bit in c output: N-bit sum s, and a -bit out c function ADD(a, b, c) for i to N do n a i b i c. two-bit sum s i n c n return c, s. out and sum 6 8 sum in out to msb of msb in signed overflow sum in out to msb of msb in signed overflow Signed overflow can occur only if the augend and addend have the same sign..2 Subtraction To subtract a subtrahend b from a minuend a, the difference d is constructed by subtracting digits one at a time from the least to the most significant digit. If in any position the resulting digit would be negative, a is ed from the next more-significant position. - - out difference A non-zero out of the most significant digit indicates unsigned overflow; the (negative) result is less than the smallest value that can be represented (zero) (-) - difference out A simpler, more convenient, and more efficient way to subtract b from a is to observe that, modulo 2 N, a b 2 N a b a (2 N b) a b

3 where b is the two s complement of b [Sec. 2..4]. Subtraction now behaves exacly like addition of signed numbers [Sec..], including the detection of signed overflow by comparing the carries in to and out of the msb. Propagating a is expensive [Sec. 5.4.]. Adding the two s complement of b to a involves propagating two separate carries (first when calculating the two s complement, and again when performing the addition with a). The first of these can be eliminated by observing that the in to the addition is always. Setting the in to instead, and then using the one s complement of b (which can be calculated very efficiently), produces exactly the same result. a b = a b (add the two s complement of b) = a b (add the one s complement of b plus ) Using this method of subtraction, the in to the lsb of the addition becomes a not in. (When c =, the subtraction yields the correct result; when c =, the subtraction yields one less than the correct result.) Similarly, the out from the msb of the addition represents the not out from the subtraction. For unsigned subtraction, an unsigned overflow has therefore occured if (and only if) the out is. (Most ALUs implement subtraction using this method. How programmers view and depends on the design of the CPU instruction set. Some CPUs, such as the ARM found in most mobile devices, use the directly and programmers must treat is as not. Others, such as Intel processors, invert the in and out when subtracting, and programmers treat as.). Multiplication To multiply a multiplicand a and multiplier b, the product p (initially ) is constructed by considering each bit position i in the multiplier. If b i =, the multiplicand is shifted left i bits (forming a partial product) and added to p [Alg..2]. NX p = b i a 2 i i= 6 5 product Signed multiplication is the same as unsigned multiplication, provided signed overflow is avoided during the addition of the partial products. The product p of two N-bit numbers p = a b can require up to 2N bits, so the mulitplication is converted to a 2N-bit multplication by sign-extending both multiplicand and multiplier to 2N bits. A 2N-bit unsigned multiplication of two signed numbers then gives the correct 2N-bit signed result.

4 Algorithm.2 Binary multiplication input: N-bit multiplicand a and multiplier b output: 2N-bit product p function MULTIPLY(a, b) p. register p is 2N bits wide for N times do if b =then p p a. accumulate partial products a a lshift b b rshift return p. product () (-5) (??) incorrect () (-5) sign extended (-5) (-) (-) sign extended (9) To obtain a N-bit result, take the least significant N bits of the 2N-bit result. If any of the most significant N bits are non-zero, then an unsigned overflow has occurred. If any of the most significant N bits differ from the sign bit p N of the result, then a signed overflow has occured..4 Division To divide a N-bit unsigned dividend a by an unsigned divisor b, set r to a and then the quotient q is the number of times b can be subtracted from r without the result becoming negative. When no more subtractions are possible, r contains the remainder and a = b q r, r<b. Because of the second condition (which implies b 6= ) there is only one solution to this equation. The manual process of long division is more efficient. quotient (cannot subtract) (-7=4) - (8-7=) 2 remainder

5 Algorithm. Unsigned division input: N-bit dividend a and divisor b output: N-bit quotient q and remainder r note: All registers are N bits wide, except for r : a which is the 2N-bit concatenation of r (most significant half) and a (least significant half). function UNSIGNEDDIVIDE(a, b) q r.r:ais the 2N-bit, zero-extended dividend for N times do q q lshift r:a r:a lshift. moves msb of dividend a to lsb of r if r b then r r b. subtract the divisor from the partial remainder q q. put the corresponding into the lsb of the quotient return q, r. unsigned quotient and remainder Manual long division can be simulated by initially shifting r (a copy of a) to the right N bits, and then building q one bit at a time, from msb to lsb. For each bit position, r is shifted left one bit and b subtracted from it. If the result is non-negative, a is appended to the least-significant end of q; otherwise a is appended to q, and r restored to its previous value. When all N bit positions have been considered, q contains a b and r contains the remainder. Signed, two s complement division can be performed by making dividend and divisor positive, performing an unsigned division, and then adjusting the signs of the quotient and remainder. As above, quotient and remainder are still defined by a = b q r, and r < b, but this is insufficient to avoid multiple solutions, because we do not know the correct signs of q and r. To make the solution unique, the usual convention is to require sign r =signa, and, if sign a =signb, sign q =, otherwise. Algorithms can be constructed to perform division directly on signed, two s complement dividend and divisor [Alg..4]. Regardless of the algorithm used, signed overflow can occur during division. For example, the two s complement signed result of the 8-bit division 28 cannot be represented in 8 bits.

6 Algorithm.4 Signed, two s complement, restoring division input: N-bit signed dividend n and divisor d output: N-bit quotient q and remainder r such that n = d q r, where r always has the same sign as n, q is negative if the signs of n and d differ, and apple r < d note: All registers are N bits wide, except for r : q which is the 2N-bit concatenation of r (most significant half) and q (least significant half). note: r : q initially holds a sign-extended dividend. Instead of shifting the divisor right at each division step, we shift the dividend r : q left (setting the lsb of q to ). The partial remainder is therefore always in r, and if we succeed in subtracting the divisor from it we can put a into the lsb of q. After N iterations, q contains the quotient and r contains the remainder. function SIGNEDDIVIDE(n, d) r:q sign-extend n. sign-extend dividend to 2N bits for N times do. form N quotient bits, one at a time, from msb to lsb r: q r: q lshift.r: q is the 2N-bit concatenation of N-bit registers r and q p r if sign r =signdthen.rand d are both positive or both negative r r d. move r towards else r r d. ditto if sign p =signq _ (r =^q =)then. subtraction did not cross q. shift a into the lsb of the quotient else. subtraction overflowed r p. restore r to previous value if r = d then. for negative n, the loop can produce r = d r. so adjust remainder and quotient if necessary q q. to guarantee r < d if sign n 6= signd then. the above computes a positive quotient q q. so make it negative if necessary return q, r. signed quotient and remainder 4

COMPUTER ARITHMETIC (Part 1)

COMPUTER ARITHMETIC (Part 1) Eastern Mediterranean University School of Computing and Technology ITEC255 Computer Organization & Architecture COMPUTER ARITHMETIC (Part 1) Introduction The two principal concerns for computer arithmetic

More information

Binary Addition. Add the binary numbers and and show the equivalent decimal addition.

Binary Addition. Add the binary numbers and and show the equivalent decimal addition. Binary Addition The rules for binary addition are 0 + 0 = 0 Sum = 0, carry = 0 0 + 1 = 0 Sum = 1, carry = 0 1 + 0 = 0 Sum = 1, carry = 0 1 + 1 = 10 Sum = 0, carry = 1 When an input carry = 1 due to a previous

More information

COMP 303 Computer Architecture Lecture 6

COMP 303 Computer Architecture Lecture 6 COMP 303 Computer Architecture Lecture 6 MULTIPLY (unsigned) Paper and pencil example (unsigned): Multiplicand 1000 = 8 Multiplier x 1001 = 9 1000 0000 0000 1000 Product 01001000 = 72 n bits x n bits =

More information

Chapter 3: part 3 Binary Subtraction

Chapter 3: part 3 Binary Subtraction Chapter 3: part 3 Binary Subtraction Iterative combinational circuits Binary adders Half and full adders Ripple carry and carry lookahead adders Binary subtraction Binary adder-subtractors Signed binary

More information

Chapter 5: Computer Arithmetic. In this chapter you will learn about:

Chapter 5: Computer Arithmetic. In this chapter you will learn about: Slide 1/29 Learning Objectives In this chapter you will learn about: Reasons for using binary instead of decimal numbers Basic arithmetic operations using binary numbers Addition (+) Subtraction (-) Multiplication

More information

Learning Objectives. Binary over Decimal. In this chapter you will learn about:

Learning Objectives. Binary over Decimal. In this chapter you will learn about: Ref Page Slide 1/29 Learning Objectives In this chapter you will learn about: Reasons for using binary instead of decimal numbers Basic arithmetic operations using binary numbers Addition (+) Subtraction

More information

Module 2: Computer Arithmetic

Module 2: Computer Arithmetic Module 2: Computer Arithmetic 1 B O O K : C O M P U T E R O R G A N I Z A T I O N A N D D E S I G N, 3 E D, D A V I D L. P A T T E R S O N A N D J O H N L. H A N N E S S Y, M O R G A N K A U F M A N N

More information

Chapter 4 Arithmetic Functions

Chapter 4 Arithmetic Functions Logic and Computer Design Fundamentals Chapter 4 Arithmetic Functions Charles Kime & Thomas Kaminski 2008 Pearson Education, Inc. (Hyperlinks are active in View Show mode) Overview Iterative combinational

More information

Digital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes

Digital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes Digital Fundamentals CHAPTER 2 Number Systems, Operations, and Codes Decimal Numbers The decimal number system has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 The decimal numbering system has a base of

More information

Chapter 5: Computer Arithmetic

Chapter 5: Computer Arithmetic Slide 1/29 Learning Objectives Computer Fundamentals: Pradeep K. Sinha & Priti Sinha In this chapter you will learn about: Reasons for using binary instead of decimal numbers Basic arithmetic operations

More information

9 Multiplication and Division

9 Multiplication and Division 9 Multiplication and Division Multiplication is done by doing shifts and additions. Multiplying two (unsigned) numbers of n bits each results in a product of 2n bits. Example: 0110 x 0011 (6x3) At start,

More information

DIGITAL ARITHMETIC: OPERATIONS AND CIRCUITS

DIGITAL ARITHMETIC: OPERATIONS AND CIRCUITS C H A P T E R 6 DIGITAL ARITHMETIC: OPERATIONS AND CIRCUITS OUTLINE 6- Binary Addition 6-2 Representing Signed Numbers 6-3 Addition in the 2 s- Complement System 6-4 Subtraction in the 2 s- Complement

More information

Lecture 8: Addition, Multiplication & Division

Lecture 8: Addition, Multiplication & Division Lecture 8: Addition, Multiplication & Division Today s topics: Signed/Unsigned Addition Multiplication Division 1 Signed / Unsigned The hardware recognizes two formats: unsigned (corresponding to the C

More information

CO212 Lecture 10: Arithmetic & Logical Unit

CO212 Lecture 10: Arithmetic & Logical Unit CO212 Lecture 10: Arithmetic & Logical Unit Shobhanjana Kalita, Dept. of CSE, Tezpur University Slides courtesy: Computer Architecture and Organization, 9 th Ed, W. Stallings Integer Representation For

More information

Number Systems and Computer Arithmetic

Number Systems and Computer Arithmetic Number Systems and Computer Arithmetic Counting to four billion two fingers at a time What do all those bits mean now? bits (011011011100010...01) instruction R-format I-format... integer data number text

More information

Chapter 10 - Computer Arithmetic

Chapter 10 - Computer Arithmetic Chapter 10 - Computer Arithmetic Luis Tarrataca luis.tarrataca@gmail.com CEFET-RJ L. Tarrataca Chapter 10 - Computer Arithmetic 1 / 126 1 Motivation 2 Arithmetic and Logic Unit 3 Integer representation

More information

EECS150 - Digital Design Lecture 13 - Combinational Logic & Arithmetic Circuits Part 3

EECS150 - Digital Design Lecture 13 - Combinational Logic & Arithmetic Circuits Part 3 EECS15 - Digital Design Lecture 13 - Combinational Logic & Arithmetic Circuits Part 3 October 8, 22 John Wawrzynek Fall 22 EECS15 - Lec13-cla3 Page 1 Multiplication a 3 a 2 a 1 a Multiplicand b 3 b 2 b

More information

The ALU consists of combinational logic. Processes all data in the CPU. ALL von Neuman machines have an ALU loop.

The ALU consists of combinational logic. Processes all data in the CPU. ALL von Neuman machines have an ALU loop. CS 320 Ch 10 Computer Arithmetic The ALU consists of combinational logic. Processes all data in the CPU. ALL von Neuman machines have an ALU loop. Signed integers are typically represented in sign-magnitude

More information

Chapter 5 : Computer Arithmetic

Chapter 5 : Computer Arithmetic Chapter 5 Computer Arithmetic Integer Representation: (Fixedpoint representation): An eight bit word can be represented the numbers from zero to 255 including = 1 = 1 11111111 = 255 In general if an nbit

More information

COMPUTER ORGANIZATION AND ARCHITECTURE

COMPUTER ORGANIZATION AND ARCHITECTURE COMPUTER ORGANIZATION AND ARCHITECTURE For COMPUTER SCIENCE COMPUTER ORGANIZATION. SYLLABUS AND ARCHITECTURE Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface,

More information

COE 202: Digital Logic Design Number Systems Part 2. Dr. Ahmad Almulhem ahmadsm AT kfupm Phone: Office:

COE 202: Digital Logic Design Number Systems Part 2. Dr. Ahmad Almulhem   ahmadsm AT kfupm Phone: Office: COE 0: Digital Logic Design Number Systems Part Dr. Ahmad Almulhem Email: ahmadsm AT kfupm Phone: 860-7554 Office: -34 Objectives Arithmetic operations: Binary number system Other number systems Base Conversion

More information

COMPUTER ARCHITECTURE AND ORGANIZATION. Operation Add Magnitudes Subtract Magnitudes (+A) + ( B) + (A B) (B A) + (A B)

COMPUTER ARCHITECTURE AND ORGANIZATION. Operation Add Magnitudes Subtract Magnitudes (+A) + ( B) + (A B) (B A) + (A B) Computer Arithmetic Data is manipulated by using the arithmetic instructions in digital computers. Data is manipulated to produce results necessary to give solution for the computation problems. The Addition,

More information

NUMBER OPERATIONS. Mahdi Nazm Bojnordi. CS/ECE 3810: Computer Organization. Assistant Professor School of Computing University of Utah

NUMBER OPERATIONS. Mahdi Nazm Bojnordi. CS/ECE 3810: Computer Organization. Assistant Professor School of Computing University of Utah NUMBER OPERATIONS Mahdi Nazm Bojnordi Assistant Professor School of Computing University of Utah CS/ECE 3810: Computer Organization Overview Homework 4 is due tonight Verify your uploaded file before the

More information

(+A) + ( B) + (A B) (B A) + (A B) ( A) + (+ B) (A B) + (B A) + (A B) (+ A) (+ B) + (A - B) (B A) + (A B) ( A) ( B) (A B) + (B A) + (A B)

(+A) + ( B) + (A B) (B A) + (A B) ( A) + (+ B) (A B) + (B A) + (A B) (+ A) (+ B) + (A - B) (B A) + (A B) ( A) ( B) (A B) + (B A) + (A B) COMPUTER ARITHMETIC 1. Addition and Subtraction of Unsigned Numbers The direct method of subtraction taught in elementary schools uses the borrowconcept. In this method we borrow a 1 from a higher significant

More information

BINARY SYSTEM. Binary system is used in digital systems because it is:

BINARY SYSTEM. Binary system is used in digital systems because it is: CHAPTER 2 CHAPTER CONTENTS 2.1 Binary System 2.2 Binary Arithmetic Operation 2.3 Signed & Unsigned Numbers 2.4 Arithmetic Operations of Signed Numbers 2.5 Hexadecimal Number System 2.6 Octal Number System

More information

ECE260: Fundamentals of Computer Engineering

ECE260: Fundamentals of Computer Engineering Arithmetic for Computers James Moscola Dept. of Engineering & Computer Science York College of Pennsylvania Based on Computer Organization and Design, 5th Edition by Patterson & Hennessy Arithmetic for

More information

Homework 3. Assigned on 02/15 Due time: midnight on 02/21 (1 WEEK only!) B.2 B.11 B.14 (hint: use multiplexors) CSCI 402: Computer Architectures

Homework 3. Assigned on 02/15 Due time: midnight on 02/21 (1 WEEK only!) B.2 B.11 B.14 (hint: use multiplexors) CSCI 402: Computer Architectures Homework 3 Assigned on 02/15 Due time: midnight on 02/21 (1 WEEK only!) B.2 B.11 B.14 (hint: use multiplexors) 1 CSCI 402: Computer Architectures Arithmetic for Computers (2) Fengguang Song Department

More information

Chapter 4 Section 2 Operations on Decimals

Chapter 4 Section 2 Operations on Decimals Chapter 4 Section 2 Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers.

More information

Semester Transition Point. EE 109 Unit 11 Binary Arithmetic. Binary Arithmetic ARITHMETIC

Semester Transition Point. EE 109 Unit 11 Binary Arithmetic. Binary Arithmetic ARITHMETIC 1 2 Semester Transition Point EE 109 Unit 11 Binary Arithmetic At this point we are going to start to transition in our class to look more at the hardware organization and the low-level software that is

More information

Divide: Paper & Pencil

Divide: Paper & Pencil Divide: Paper & Pencil 1001 Quotient Divisor 1000 1001010 Dividend -1000 10 101 1010 1000 10 Remainder See how big a number can be subtracted, creating quotient bit on each step Binary => 1 * divisor or

More information

CPS 104 Computer Organization and Programming

CPS 104 Computer Organization and Programming CPS 104 Computer Organization and Programming Lecture 9: Integer Arithmetic. Robert Wagner CPS104 IMD.1 RW Fall 2000 Overview of Today s Lecture: Integer Multiplication and Division. Read Appendix B CPS104

More information

More complicated than addition. Let's look at 3 versions based on grade school algorithm (multiplicand) More time and more area

More complicated than addition. Let's look at 3 versions based on grade school algorithm (multiplicand) More time and more area Multiplication More complicated than addition accomplished via shifting and addition More time and more area Let's look at 3 versions based on grade school algorithm 01010010 (multiplicand) x01101101 (multiplier)

More information

CS/COE 0447 Example Problems for Exam 2 Spring 2011

CS/COE 0447 Example Problems for Exam 2 Spring 2011 CS/COE 0447 Example Problems for Exam 2 Spring 2011 1) Show the steps to multiply the 4-bit numbers 3 and 5 with the fast shift-add multipler. Use the table below. List the multiplicand (M) and product

More information

DLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR

DLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR UNIT I Digital Systems: Binary Numbers, Octal, Hexa Decimal and other base numbers, Number base conversions, complements, signed binary numbers, Floating point number representation, binary codes, error

More information

Numbering systems. Dr Abu Arqoub

Numbering systems. Dr Abu Arqoub Numbering systems The decimal numbering system is widely used, because the people Accustomed (معتاد) to use the hand fingers in their counting. But with the development of the computer science another

More information

Organisasi Sistem Komputer

Organisasi Sistem Komputer LOGO Organisasi Sistem Komputer OSK 8 Aritmatika Komputer 1 1 PT. Elektronika FT UNY Does the calculations Arithmetic & Logic Unit Everything else in the computer is there to service this unit Handles

More information

Week 7: Assignment Solutions

Week 7: Assignment Solutions Week 7: Assignment Solutions 1. In 6-bit 2 s complement representation, when we subtract the decimal number +6 from +3, the result (in binary) will be: a. 111101 b. 000011 c. 100011 d. 111110 Correct answer

More information

Math in MIPS. Subtracting a binary number from another binary number also bears an uncanny resemblance to the way it s done in decimal.

Math in MIPS. Subtracting a binary number from another binary number also bears an uncanny resemblance to the way it s done in decimal. Page < 1 > Math in MIPS Adding and Subtracting Numbers Adding two binary numbers together is very similar to the method used with decimal numbers, except simpler. When you add two binary numbers together,

More information

CHAPTER V NUMBER SYSTEMS AND ARITHMETIC

CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V-1 CHAPTER V CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V-2 NUMBER SYSTEMS RADIX-R REPRESENTATION Decimal number expansion 73625 10 = ( 7 10 4 ) + ( 3 10 3 ) + ( 6 10 2 ) + ( 2 10 1 ) +(

More information

Number System. Introduction. Decimal Numbers

Number System. Introduction. Decimal Numbers Number System Introduction Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26

More information

Kinds Of Data CHAPTER 3 DATA REPRESENTATION. Numbers Are Different! Positional Number Systems. Text. Numbers. Other

Kinds Of Data CHAPTER 3 DATA REPRESENTATION. Numbers Are Different! Positional Number Systems. Text. Numbers. Other Kinds Of Data CHAPTER 3 DATA REPRESENTATION Numbers Integers Unsigned Signed Reals Fixed-Point Floating-Point Binary-Coded Decimal Text ASCII Characters Strings Other Graphics Images Video Audio Numbers

More information

World Inside a Computer is Binary

World Inside a Computer is Binary C Programming 1 Representation of int data World Inside a Computer is Binary C Programming 2 Decimal Number System Basic symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Radix-10 positional number system. The radix

More information

CHW 261: Logic Design

CHW 261: Logic Design CHW 261: Logic Design Instructors: Prof. Hala Zayed Dr. Ahmed Shalaby http://www.bu.edu.eg/staff/halazayed14 http://bu.edu.eg/staff/ahmedshalaby14# Slide 1 Slide 2 Slide 3 Digital Fundamentals CHAPTER

More information

EEC 483 Computer Organization

EEC 483 Computer Organization EEC 483 Computer Organization Chapter 3. Arithmetic for Computers Chansu Yu Table of Contents Ch.1 Introduction Ch. 2 Instruction: Machine Language Ch. 3-4 CPU Implementation Ch. 5 Cache and VM Ch. 6-7

More information

Integer Multiplication and Division

Integer Multiplication and Division Integer Multiplication and Division COE 301 Computer Organization Prof. Muhamed Mudawar College of Computer Sciences and Engineering King Fahd University of Petroleum and Minerals Presentation Outline

More information

Timing for Ripple Carry Adder

Timing for Ripple Carry Adder Timing for Ripple Carry Adder 1 2 3 Look Ahead Method 5 6 7 8 9 Look-Ahead, bits wide 10 11 Multiplication Simple Gradeschool Algorithm for 32 Bits (6 Bit Result) Multiplier Multiplicand AND gates 32

More information

EE 109 Unit 6 Binary Arithmetic

EE 109 Unit 6 Binary Arithmetic EE 109 Unit 6 Binary Arithmetic 1 2 Semester Transition Point At this point we are going to start to transition in our class to look more at the hardware organization and the low-level software that is

More information

UNIT-III COMPUTER ARTHIMETIC

UNIT-III COMPUTER ARTHIMETIC UNIT-III COMPUTER ARTHIMETIC INTRODUCTION Arithmetic Instructions in digital computers manipulate data to produce results necessary for the of activity solution of computational problems. These instructions

More information

2.1. Unit 2. Integer Operations (Arithmetic, Overflow, Bitwise Logic, Shifting)

2.1. Unit 2. Integer Operations (Arithmetic, Overflow, Bitwise Logic, Shifting) 2.1 Unit 2 Integer Operations (Arithmetic, Overflow, Bitwise Logic, Shifting) 2.2 Skills & Outcomes You should know and be able to apply the following skills with confidence Perform addition & subtraction

More information

Chapter 3: Arithmetic for Computers

Chapter 3: Arithmetic for Computers Chapter 3: Arithmetic for Computers Objectives Signed and Unsigned Numbers Addition and Subtraction Multiplication and Division Floating Point Computer Architecture CS 35101-002 2 The Binary Numbering

More information

Korea University of Technology and Education

Korea University of Technology and Education MEC52 디지털공학 Binary Systems Jee-Hwan Ryu School of Mechanical Engineering Binary Numbers a 5 a 4 a 3 a 2 a a.a - a -2 a -3 base or radix = a n r n a n- r n-...a 2 r 2 a ra a - r - a -2 r -2...a -m r -m

More information

Number Systems. Both numbers are positive

Number Systems. Both numbers are positive Number Systems Range of Numbers and Overflow When arithmetic operation such as Addition, Subtraction, Multiplication and Division are performed on numbers the results generated may exceed the range of

More information

Iterative Division Techniques COMPUTER ARITHMETIC: Lecture Notes # 6. University of Illinois at Chicago

Iterative Division Techniques COMPUTER ARITHMETIC: Lecture Notes # 6. University of Illinois at Chicago 1 ECE 368 CAD Based Logic Design Instructor: Shantanu Dutt Department of Electrical and Computer Engineering University of Illinois at Chicago Lecture Notes # 6 COMPUTER ARITHMETIC: Iterative Division

More information

COMPUTER ORGANIZATION AND. Edition. The Hardware/Software Interface. Chapter 3. Arithmetic for Computers

COMPUTER ORGANIZATION AND. Edition. The Hardware/Software Interface. Chapter 3. Arithmetic for Computers ARM D COMPUTER ORGANIZATION AND Edition The Hardware/Software Interface Chapter 3 Arithmetic for Computers Modified and extended by R.J. Leduc - 2016 In this chapter, we will investigate: How integer arithmetic

More information

DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM

DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM COURSE / CODE DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) NUMBER SYSTEM A considerable subset of digital systems deals with arithmetic operations. To understand the

More information

By, Ajinkya Karande Adarsh Yoga

By, Ajinkya Karande Adarsh Yoga By, Ajinkya Karande Adarsh Yoga Introduction Early computer designers believed saving computer time and memory were more important than programmer time. Bug in the divide algorithm used in Intel chips.

More information

Arithmetic Processing

Arithmetic Processing CS/EE 5830/6830 VLSI ARCHITECTURE Chapter 1 Basic Number Representations and Arithmetic Algorithms Arithmetic Processing AP = (operands, operation, results, conditions, singularities) Operands are: Set

More information

University of Illinois at Chicago. Lecture Notes # 13

University of Illinois at Chicago. Lecture Notes # 13 1 ECE 366 Computer Architecture Instructor: Shantanu Dutt Department of Electrical and Computer Engineering University of Illinois at Chicago Lecture Notes # 13 COMPUTER ARITHMETIC: Iterative Division

More information

Arithmetic Logic Unit

Arithmetic Logic Unit Arithmetic Logic Unit A.R. Hurson Department of Computer Science Missouri University of Science & Technology A.R. Hurson 1 Arithmetic Logic Unit It is a functional bo designed to perform "basic" arithmetic,

More information

Tailoring the 32-Bit ALU to MIPS

Tailoring the 32-Bit ALU to MIPS Tailoring the 32-Bit ALU to MIPS MIPS ALU extensions Overflow detection: Carry into MSB XOR Carry out of MSB Branch instructions Shift instructions Slt instruction Immediate instructions ALU performance

More information

Chapter 2. Positional number systems. 2.1 Signed number representations Signed magnitude

Chapter 2. Positional number systems. 2.1 Signed number representations Signed magnitude Chapter 2 Positional number systems A positional number system represents numeric values as sequences of one or more digits. Each digit in the representation is weighted according to its position in the

More information

Number System. Introduction. Natural Numbers (N) Whole Numbers (W) Integers (Z) Prime Numbers (P) Face Value. Place Value

Number System. Introduction. Natural Numbers (N) Whole Numbers (W) Integers (Z) Prime Numbers (P) Face Value. Place Value 1 Number System Introduction In this chapter, we will study about the number system and number line. We will also learn about the four fundamental operations on whole numbers and their properties. Natural

More information

EE260: Logic Design, Spring n Integer multiplication. n Booth s algorithm. n Integer division. n Restoring, non-restoring

EE260: Logic Design, Spring n Integer multiplication. n Booth s algorithm. n Integer division. n Restoring, non-restoring EE 260: Introduction to Digital Design Arithmetic II Yao Zheng Department of Electrical Engineering University of Hawaiʻi at Mānoa Overview n Integer multiplication n Booth s algorithm n Integer division

More information

D I G I T A L C I R C U I T S E E

D I G I T A L C I R C U I T S E E D I G I T A L C I R C U I T S E E Digital Circuits Basic Scope and Introduction This book covers theory solved examples and previous year gate question for following topics: Number system, Boolean algebra,

More information

CHAPTER 6 ARITHMETIC, LOGIC INSTRUCTIONS, AND PROGRAMS

CHAPTER 6 ARITHMETIC, LOGIC INSTRUCTIONS, AND PROGRAMS CHAPTER 6 ARITHMETIC, LOGIC INSTRUCTIONS, AND PROGRAMS Addition of Unsigned Numbers The instruction ADD is used to add two operands Destination operand is always in register A Source operand can be a register,

More information

CS/COE0447: Computer Organization

CS/COE0447: Computer Organization CS/COE0447: Computer Organization and Assembly Language Chapter 3 Sangyeun Cho Dept. of Computer Science Five classic components I am like a control tower I am like a pack of file folders I am like a conveyor

More information

CS/COE0447: Computer Organization

CS/COE0447: Computer Organization Five classic components CS/COE0447: Computer Organization and Assembly Language I am like a control tower I am like a pack of file folders Chapter 3 I am like a conveyor belt + service stations I exchange

More information

Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Lecture 3

Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Lecture 3 Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Instructor: Nicole Hynes nicole.hynes@rutgers.edu 1 Fixed Point Numbers Fixed point number: integer part

More information

CS 5803 Introduction to High Performance Computer Architecture: Arithmetic Logic Unit. A.R. Hurson 323 CS Building, Missouri S&T

CS 5803 Introduction to High Performance Computer Architecture: Arithmetic Logic Unit. A.R. Hurson 323 CS Building, Missouri S&T CS 5803 Introduction to High Performance Computer Architecture: Arithmetic Logic Unit A.R. Hurson 323 CS Building, Missouri S&T hurson@mst.edu 1 Outline Motivation Design of a simple ALU How to design

More information

361 div.1. Computer Architecture EECS 361 Lecture 7: ALU Design : Division

361 div.1. Computer Architecture EECS 361 Lecture 7: ALU Design : Division 361 div.1 Computer Architecture EECS 361 Lecture 7: ALU Design : Division Outline of Today s Lecture Introduction to Today s Lecture Divide Questions and Administrative Matters Introduction to Single cycle

More information

CS 64 Week 1 Lecture 1. Kyle Dewey

CS 64 Week 1 Lecture 1. Kyle Dewey CS 64 Week 1 Lecture 1 Kyle Dewey Overview Bitwise operation wrap-up Two s complement Addition Subtraction Multiplication (if time) Bitwise Operation Wrap-up Shift Left Move all the bits N positions to

More information

UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS

UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS (09 periods) Computer Arithmetic: Data Representation, Fixed Point Representation, Floating Point Representation, Addition and

More information

Arithmetic for Computers

Arithmetic for Computers MIPS Arithmetic Instructions Cptr280 Dr Curtis Nelson Arithmetic for Computers Operations on integers Addition and subtraction; Multiplication and division; Dealing with overflow; Signed vs. unsigned numbers.

More information

NUMBER SCALING FOR THE LGP-27

NUMBER SCALING FOR THE LGP-27 NUMBER SCALING FOR THE LGP-27 5 SCALING The LGP-21 considers all numbers to be within the range -l

More information

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) WHOLE NUMBERS REVIEW A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money,

More information

Data Representation in Digital Computers

Data Representation in Digital Computers Data Representation in Digital Computers The material presented herein is excerpted from a series of lecture slides originally prepared by David Lowther and Peet Silvester for their textbook Computer Engineering.

More information

Chapter 10 Binary Arithmetics

Chapter 10 Binary Arithmetics 27..27 Chapter Binary Arithmetics Dr.-Ing. Stefan Werner Table of content Chapter : Switching Algebra Chapter 2: Logical Levels, Timing & Delays Chapter 3: Karnaugh-Veitch-Maps Chapter 4: Combinational

More information

CO Computer Architecture and Programming Languages CAPL. Lecture 9

CO Computer Architecture and Programming Languages CAPL. Lecture 9 CO20-320241 Computer Architecture and Programming Languages CAPL Lecture 9 Dr. Kinga Lipskoch Fall 2017 A Four-bit Number Circle CAPL Fall 2017 2 / 38 Functional Parts of an ALU CAPL Fall 2017 3 / 38 Addition

More information

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Arithmetic (a) The four possible cases Carry (b) Truth table x y

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Arithmetic (a) The four possible cases Carry (b) Truth table x y Arithmetic A basic operation in all digital computers is the addition and subtraction of two numbers They are implemented, along with the basic logic functions such as AND,OR, NOT,EX- OR in the ALU subsystem

More information

Binary Adders. Ripple-Carry Adder

Binary Adders. Ripple-Carry Adder Ripple-Carry Adder Binary Adders x n y n x y x y c n FA c n - c 2 FA c FA c s n MSB position Longest delay (Critical-path delay): d c(n) = n d carry = 2n gate delays d s(n-) = (n-) d carry +d sum = 2n

More information

Chapter 3 Arithmetic for Computers. ELEC 5200/ From P-H slides

Chapter 3 Arithmetic for Computers. ELEC 5200/ From P-H slides Chapter 3 Arithmetic for Computers 1 Arithmetic for Computers Operations on integers Addition and subtraction Multiplication and division Dealing with overflow Floating-point real numbers Representation

More information

Positional Number System

Positional Number System Positional Number System A number is represented by a string of digits where each digit position has an associated weight. The weight is based on the radix of the number system. Some common radices: Decimal.

More information

Outline. EEL-4713 Computer Architecture Multipliers and shifters. Deriving requirements of ALU. MIPS arithmetic instructions

Outline. EEL-4713 Computer Architecture Multipliers and shifters. Deriving requirements of ALU. MIPS arithmetic instructions Outline EEL-4713 Computer Architecture Multipliers and shifters Multiplication and shift registers Chapter 3, section 3.4 Next lecture Division, floating-point 3.5 3.6 EEL-4713 Ann Gordon-Ross.1 EEL-4713

More information

Internal Data Representation

Internal Data Representation Appendices This part consists of seven appendices, which provide a wealth of reference material. Appendix A primarily discusses the number systems and their internal representation. Appendix B gives information

More information

Computer Arithmetic Ch 8

Computer Arithmetic Ch 8 Computer Arithmetic Ch 8 ALU Integer Representation Integer Arithmetic Floating-Point Representation Floating-Point Arithmetic 1 Arithmetic Logical Unit (ALU) (2) (aritmeettis-looginen yksikkö) Does all

More information

COMP 122/L Lecture 2. Kyle Dewey

COMP 122/L Lecture 2. Kyle Dewey COMP 122/L Lecture 2 Kyle Dewey Outline Operations on binary values AND, OR, XOR, NOT Bit shifting (left, two forms of right) Addition Subtraction Twos complement Bitwise Operations Bitwise AND Similar

More information

Computer Arithmetic Ch 8

Computer Arithmetic Ch 8 Computer Arithmetic Ch 8 ALU Integer Representation Integer Arithmetic Floating-Point Representation Floating-Point Arithmetic 1 Arithmetic Logical Unit (ALU) (2) Does all work in CPU (aritmeettis-looginen

More information

Introduction to Digital Logic Missouri S&T University CPE 2210 Multipliers/Dividers

Introduction to Digital Logic Missouri S&T University CPE 2210 Multipliers/Dividers Introduction to Digital Logic Missouri S&T University CPE 2210 Multipliers/Dividers Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science

More information

Adding Binary Integers. Part 5. Adding Base 10 Numbers. Adding 2's Complement. Adding Binary Example = 10. Arithmetic Logic Unit

Adding Binary Integers. Part 5. Adding Base 10 Numbers. Adding 2's Complement. Adding Binary Example = 10. Arithmetic Logic Unit Part 5 Adding Binary Integers Arithmetic Logic Unit = Adding Binary Integers Adding Base Numbers Computer's add binary numbers the same way that we do with decimal Columns are aligned, added, and "'s"

More information

Adding Binary Integers. Part 4. Negative Binary. Integers. Adding Base 10 Numbers. Adding Binary Example = 10. Arithmetic Logic Unit

Adding Binary Integers. Part 4. Negative Binary. Integers. Adding Base 10 Numbers. Adding Binary Example = 10. Arithmetic Logic Unit Part 4 Adding Binary Integers Arithmetic Logic Unit = Adding Binary Integers Adding Base Numbers Computer's add binary numbers the same way that we do with decimal Columns are aligned, added, and "'s"

More information

5.OA Why Do We Need an Order of Operations?

5.OA Why Do We Need an Order of Operations? 5.OA Why Do We Need an Order of Operations? Alignments to Content Standards: 5.OA.A Task a. State the meaning of each of the following expressions and draw a picture that represents it. b. State the meaning

More information

MIPS Integer ALU Requirements

MIPS Integer ALU Requirements MIPS Integer ALU Requirements Add, AddU, Sub, SubU, AddI, AddIU: 2 s complement adder/sub with overflow detection. And, Or, Andi, Ori, Xor, Xori, Nor: Logical AND, logical OR, XOR, nor. SLTI, SLTIU (set

More information

Arithmetic Operations on Binary Numbers

Arithmetic Operations on Binary Numbers Arithmetic Operations on Binary Numbers Because of its widespread use, we will concentrate on addition and subtraction for Two's Complement representation. The nice feature with Two's Complement is that

More information

Arithmetic Operations

Arithmetic Operations Arithmetic Operations Arithmetic Operations addition subtraction multiplication division Each of these operations on the integer representations: unsigned two's complement 1 Addition One bit of binary

More information

Chapter 4. Combinational Logic

Chapter 4. Combinational Logic Chapter 4. Combinational Logic Tong In Oh 1 4.1 Introduction Combinational logic: Logic gates Output determined from only the present combination of inputs Specified by a set of Boolean functions Sequential

More information

Number Systems CHAPTER Positional Number Systems

Number Systems CHAPTER Positional Number Systems CHAPTER 2 Number Systems Inside computers, information is encoded as patterns of bits because it is easy to construct electronic circuits that exhibit the two alternative states, 0 and 1. The meaning of

More information

Integer Arithmetic. Jinkyu Jeong Computer Systems Laboratory Sungkyunkwan University

Integer Arithmetic. Jinkyu Jeong Computer Systems Laboratory Sungkyunkwan University Integer Arithmetic Jinkyu Jeong (jinkyu@skku.edu) Computer Systems Laboratory Sungkyunkwan University http://csl.skku.edu EEE3050: Theory on Computer Architectures, Spring 2017, Jinkyu Jeong (jinkyu@skku.edu)

More information

Arithmetic and Logical Operations

Arithmetic and Logical Operations Arithmetic and Logical Operations 2 CMPE2c x +y + sum Or in tabular form Binary Addition Carry Out Sum B A Carry In Binary Addition And as a full adder a b co ci sum 4-bit Ripple-Carry adder: Carry values

More information

Groups of two-state devices are used to represent data in a computer. In general, we say the states are either: high/low, on/off, 1/0,...

Groups of two-state devices are used to represent data in a computer. In general, we say the states are either: high/low, on/off, 1/0,... Chapter 9 Computer Arithmetic Reading: Section 9.1 on pp. 290-296 Computer Representation of Data Groups of two-state devices are used to represent data in a computer. In general, we say the states are

More information

A complement number system is used to represent positive and negative integers. A complement number system is based on a fixed length representation

A complement number system is used to represent positive and negative integers. A complement number system is based on a fixed length representation Complement Number Systems A complement number system is used to represent positive and negative integers A complement number system is based on a fixed length representation of numbers Pretend that integers

More information