4/8/17. Admin. Assignment 5 BINARY. David Kauchak CS 52 Spring 2017

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "4/8/17. Admin. Assignment 5 BINARY. David Kauchak CS 52 Spring 2017"

Transcription

1 4/8/17 Admin! Assignment 5 BINARY David Kauchak CS 52 Spring 2017 Diving into your computer Normal computer user 1

2 After intro CS After 5 weeks of cs52 What now One last note on CS52 memory address binary representation of code How do we get this instructions (assembly code) 2

3 Encoding assembly instructions Binary numbers revisited What number does 1001 represent in binary opcode rx ry rz Depends! Is it a signed number or If signed, what convention are we using Twos complement Twos complement For a number with n digits the high order bit represents -2 n-1 What number is it signed (twos complement) signed (twos complement)

4 Twos complement Twos complement What number is it What number is it signed (twos complement) signed (twos complement) Twos complement How many numbers can we represent with each approach using 4 bits 16 (2 4 ) numbers, 0000, 0001,., 1111 Doesn t matter the representation! Twos complement How many numbers can we represent with each approach using 32 bits billion numbers signed (twos complement) signed (twos complement)

5 Twos complement What is the range of numbers that we can represent for each approach with 4 bits : 0, 1, 15 signed: -8, -7,, 7 signed (twos complement) binary representation binary representation twos complement binary representation twos complement

6 binary representation twos complement binary representation twos complement binary representation twos complement How can you tell if a number is negative binary representation twos complement High order bit! 6

7 A two s complement trick You can also calculate the value of a negative number represented as twos complement as follows:! Flip all of the bits (0 " 1 and 1" 0)! Add 1! The resulting number is the magnitude of the original negative number A two s complement trick You can also calculate the value of a negative number represented as twos complement as follows:! Flip all of the bits (0 " 1 and 1" 0)! Add 1! The resulting number is the magnitude of the original negative number flip the bits add flip the bits add Shifting Shifting 37 >> 2 number to be shifted right shift number of positions to shift 7

8 Shifting Shifting 37 >> 2 37 >> shift right two positions decimal form Shifting Shifting with fixed bit representations In real computers, we generally have a fixed number of bits we use to represent a number (e.g. 8-bits, 16-bits, 32-bits) 37 >> shift right three positions decimal form 8

9 Shifting 8-bit numbers 37 pad with 0s 37 >> 2 What is 37 as an 8-bit binary number Shifting 8-bit numbers >> 2 How do we fill in the leftmost bits shift right two positions Shifting 8-bit numbers 37 >> 2 Shifting 8-bit numbers 37 >> 2 How do we fill in the leftmost bits shift right two positions shift right two positions (discard away bits shifting off) decimal form 9

10 Shifting 8-bit numbers 15 << 2 Shifting 8-bit numbers 15 << 2 15 Shifting 8-bit numbers 15 << 2 Shifting 8-bit numbers 15 << shift left two positions 10

11 Shifting 8-bit numbers 15 << 2 Shifting 8-bit numbers 15 << shift left two positions shift left two positions Shifting 8-bit numbers 15 << 2 Shifting mathematically What does left shifting by one position do mathematically 0 A B C shift left two positions decimal form 11

12 Shifting mathematically What does left shifting by one position do mathematically Shifting mathematically What does left shifting by one position do mathematically 0 A B C 0 A B C = A * B * C * 2 0 A B C 0 A B C 0 = A * B * C * 2 1 = 2 *(A * B * C * 2 0 ) Shifting mathematically What does left shifting by one position do mathematically Shifting mathematically What does left shifting by n positions do mathematically 0 A B C = A * B * C * 2 0 Doubles the number! Multiply by 2 n (double n times) A B C 0 = A * B * C * 2 1 = 2 *(A * B * C * 2 0 ) 12

13 Shifting mathematically What does right shifting by one position do mathematically 0 A B C Shifting mathematically What does right shifting by one position do mathematically 0 A B C 0 0 A B Shifting mathematically What does right shifting by one position do mathematically Shifting mathematically What does right shifting by one position do mathematically 0 A B C = A * B * C * A B C = A * B * C * 2 0 Integer divide by A B = A * B * 2 0 = (A * B * C * 2 0 ) div A B = A * B * 2 0 = (A * B * C * 2 0 ) div 2 13

14 Shifting mathematically What does right shifting by n positions do mathematically Integer division by 2 n (halve n times) >> 1 >> 1 What is as a 4-bit binary number >> 1 How do we fill in the leftmost bit shift right one position 14

15 Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit shift right one position shift right one position Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit >> shift right one position shift right one position decimal form 15

16 Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit >> 1 >> shift right one position decimal form Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit >> 2 Arithmetic shifting mathematically What does right arithmetic shifting by n positions do mathematically for signed numbers Integer division by 2 n (halve n times) Same thing!! shift right two positions decimal form 16

17 Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit shift right one position shift right one position Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit >>> 1 Two types of right shifts: - arithmetic shift: shift in the same as the highorder bit >>> shift right one position decimal form shift right one position decimal form 17

18 Left shifts Two types of left shifts - arithmetic shift: Left shifts Two types of left shifts - arithmetic shift: arithmetic -3 << 1 arithmetic -3 << (double the number) logical -3 <<< 1 logical -3 <<< Left shifts Two types of left shifts - arithmetic shift: arithmetic logical -3 << 1-3 <<< Only one type of left shift (double the number) Shifting summarized Arithmetic shift:! Right shift n # shift n bits to the right # discard right n bits # left n bits match high-order bits of original number # Effect: Integer division by 2 n (halve n times)! Left shift # shift n bits to the left # discard left n bits # right n bits are 0s # Effect: multiply by 2 n (double n times) Logical shift right:! left n bits are 0s (no mathematical guarantees for negative numbers) 18

19 Adding numbers base 10 Adding numbers base 10 Add: 456 and Adding numbers base 10 Adding numbers base Add: and

20 Adding numbers base 5 Adding numbers base Adding numbers base 5 Adding numbers base Add: and

21 Adding numbers base 2 Adding numbers base Adding numbers base 2 Addition with 4-bit twos complement numbers

22 Addition with 4-bit twos complement numbers Addition with 4-bit twos complement numbers (Note: I m going to stop writing the base 2 ) Addition with 4-bit twos complement numbers Addition with 4-bit twos complement numbers (11 ) Overflow! We cannot represent this number (it s too large) 22

23 Addition with 4-bit twos complement numbers Addition with 4-bit twos complement numbers Addition with 4-bit twos complement numbers Subtraction ignore the last carry Ideas 23

24 Subtraction Negate the 2 nd number (flip the bits and add 1) Add them! Midterm Average: 28 (77%) Q1: 24.9 (70%) Median: 28.5 (81%) Q3: 32 (91%) 24

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

1010 2?= ?= CS 64 Lecture 2 Data Representation. Decimal Numbers: Base 10. Reading: FLD Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

1010 2?= ?= CS 64 Lecture 2 Data Representation. Decimal Numbers: Base 10. Reading: FLD Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 CS 64 Lecture 2 Data Representation Reading: FLD 1.2-1.4 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 ) + (1x10 0 ) 1010 10?= 1010 2?= 1

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

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning 4 Operations On Data 4.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List the three categories of operations performed on data.

More information

Digital Arithmetic. Digital Arithmetic: Operations and Circuits Dr. Farahmand

Digital Arithmetic. Digital Arithmetic: Operations and Circuits Dr. Farahmand Digital Arithmetic Digital Arithmetic: Operations and Circuits Dr. Farahmand Binary Arithmetic Digital circuits are frequently used for arithmetic operations Fundamental arithmetic operations on binary

More information

Octal and Hexadecimal Integers

Octal and Hexadecimal Integers Octal and Hexadecimal Integers CS 350: Computer Organization & Assembler Language Programming A. Why? Octal and hexadecimal numbers are useful for abbreviating long bitstrings. Some operations on octal

More information

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning 4 Operations On Data 4.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List the three categories of operations performed on data.

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

CS2630: Computer Organization Homework 1 Bits, bytes, and memory organization Due January 25, 2017, 11:59pm

CS2630: Computer Organization Homework 1 Bits, bytes, and memory organization Due January 25, 2017, 11:59pm CS2630: Computer Organization Homework 1 Bits, bytes, and memory organization Due January 25, 2017, 11:59pm Instructions: Show your work. Correct answers with no work will not receive full credit. Whether

More information

Signed umbers. Sign/Magnitude otation

Signed umbers. Sign/Magnitude otation Signed umbers So far we have discussed unsigned number representations. In particular, we have looked at the binary number system and shorthand methods in representing binary codes. With m binary digits,

More information

ENE 334 Microprocessors

ENE 334 Microprocessors Page 1 ENE 334 Microprocessors Lecture 10: MCS-51: Logical and Arithmetic : Dejwoot KHAWPARISUTH http://webstaff.kmutt.ac.th/~dejwoot.kha/ ENE 334 MCS-51 Logical & Arithmetic Page 2 Logical: Objectives

More information

Fundamentals of Programming Session 2

Fundamentals of Programming Session 2 Fundamentals of Programming Session 2 Instructor: Reza Entezari-Maleki Email: entezari@ce.sharif.edu 1 Fall 2013 Sharif University of Technology Outlines Programming Language Binary numbers Addition Subtraction

More information

Arithmetic and Bitwise Operations on Binary Data

Arithmetic and Bitwise Operations on Binary Data Arithmetic and Bitwise Operations on Binary Data CSCI 224 / ECE 317: Computer Architecture Instructor: Prof. Jason Fritts Slides adapted from Bryant & O Hallaron s slides 1 Boolean Algebra Developed by

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

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation Course Schedule CS 221 Computer Architecture Week 3: Information Representation (2) Fall 2001 W1 Sep 11- Sep 14 Introduction W2 Sep 18- Sep 21 Information Representation (1) (Chapter 3) W3 Sep 25- Sep

More information

Lecture 2: Number Systems

Lecture 2: Number Systems Lecture 2: Number Systems Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Prof. Russell Tessier of University of Massachusetts Aby George of Wayne State University Contents

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

Floating Point. The World is Not Just Integers. Programming languages support numbers with fraction

Floating Point. The World is Not Just Integers. Programming languages support numbers with fraction 1 Floating Point The World is Not Just Integers Programming languages support numbers with fraction Called floating-point numbers Examples: 3.14159265 (π) 2.71828 (e) 0.000000001 or 1.0 10 9 (seconds in

More information

CS101 Lecture 04: Binary Arithmetic

CS101 Lecture 04: Binary Arithmetic CS101 Lecture 04: Binary Arithmetic Binary Number Addition Two s complement encoding Briefly: real number representation Aaron Stevens (azs@bu.edu) 25 January 2013 What You ll Learn Today Counting in binary

More information

Lecture 6: Signed Numbers & Arithmetic Circuits. BCD (Binary Coded Decimal) Points Addressed in this Lecture

Lecture 6: Signed Numbers & Arithmetic Circuits. BCD (Binary Coded Decimal) Points Addressed in this Lecture Points ddressed in this Lecture Lecture 6: Signed Numbers rithmetic Circuits Professor Peter Cheung Department of EEE, Imperial College London (Floyd 2.5-2.7, 6.1-6.7) (Tocci 6.1-6.11, 9.1-9.2, 9.4) Representing

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

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

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

Inf2C - Computer Systems Lecture 2 Data Representation

Inf2C - Computer Systems Lecture 2 Data Representation Inf2C - Computer Systems Lecture 2 Data Representation Boris Grot School of Informatics University of Edinburgh Last lecture Moore s law Types of computer systems Computer components Computer system stack

More information

Computer Architecture and Organization

Computer Architecture and Organization 3-1 Chapter 3 - Arithmetic Computer Architecture and Organization Miles Murdocca and Vincent Heuring Chapter 3 Arithmetic 3-2 Chapter 3 - Arithmetic Chapter Contents 3.1 Fixed Point Addition and Subtraction

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

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

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

Signed Binary Numbers

Signed Binary Numbers Signed Binary Numbers Unsigned Binary Numbers We write numbers with as many digits as we need: 0, 99, 65536, 15000, 1979, However, memory locations and CPU registers always hold a constant, fixed number

More information

The type of all data used in a C (or C++) program must be specified

The type of all data used in a C (or C++) program must be specified The type of all data used in a C (or C++) program must be specified A data type is a description of the data being represented That is, a set of possible values and a set of operations on those values

More information

Chapter 2 Bits, Data Types, and Operations

Chapter 2 Bits, Data Types, and Operations Chapter 2 Bits, Data Types, and Operations How do we represent data in a computer? At the lowest level, a computer is an electronic machine. works by controlling the flow of electrons Easy to recognize

More information

CS/EE1012 INTRODUCTION TO COMPUTER ENGINEERING SPRING 2013 HOMEWORK I. Solve all homework and exam problems as shown in class and sample solutions

CS/EE1012 INTRODUCTION TO COMPUTER ENGINEERING SPRING 2013 HOMEWORK I. Solve all homework and exam problems as shown in class and sample solutions CS/EE2 INTRODUCTION TO COMPUTER ENGINEERING SPRING 23 DUE : February 22, 23 HOMEWORK I READ : Related portions of the following chapters : È Chapter È Chapter 2 È Appendix E ASSIGNMENT : There are eight

More information

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng.

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng. CS 265 Computer Architecture Wei Lu, Ph.D., P.Eng. 1 Part 1: Data Representation Our goal: revisit and re-establish fundamental of mathematics for the computer architecture course Overview: what are bits

More information

Computer Organization CS 206 T Lec# 2: Instruction Sets

Computer Organization CS 206 T Lec# 2: Instruction Sets Computer Organization CS 206 T Lec# 2: Instruction Sets Topics What is an instruction set Elements of instruction Instruction Format Instruction types Types of operations Types of operand Addressing mode

More information

9/23/15. Agenda. Goals of this Lecture. For Your Amusement. Number Systems and Number Representation. The Binary Number System

9/23/15. Agenda. Goals of this Lecture. For Your Amusement. Number Systems and Number Representation. The Binary Number System For Your Amusement Number Systems and Number Representation Jennifer Rexford Question: Why do computer programmers confuse Christmas and Halloween? Answer: Because 25 Dec = 31 Oct -- http://www.electronicsweekly.com

More information

BITWISE OPERATORS. There are a number of ways to manipulate binary values. Just as you can with

BITWISE OPERATORS. There are a number of ways to manipulate binary values. Just as you can with BITWISE OPERATORS There are a number of ways to manipulate binary values. Just as you can with decimal numbers, you can perform standard mathematical operations - addition, subtraction, multiplication,

More information

Number Systems. Binary Numbers. Appendix. Decimal notation represents numbers as powers of 10, for example

Number Systems. Binary Numbers. Appendix. Decimal notation represents numbers as powers of 10, for example Appendix F Number Systems Binary Numbers Decimal notation represents numbers as powers of 10, for example 1729 1 103 7 102 2 101 9 100 decimal = + + + There is no particular reason for the choice of 10,

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

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

Principles of Computer Architecture. Chapter 3: Arithmetic

Principles of Computer Architecture. Chapter 3: Arithmetic 3-1 Chapter 3 - Arithmetic Principles of Computer Architecture Miles Murdocca and Vincent Heuring Chapter 3: Arithmetic 3-2 Chapter 3 - Arithmetic 3.1 Overview Chapter Contents 3.2 Fixed Point Addition

More information

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.

DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors. Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic 0 (0 volts) and one for logic

More information

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010 Contents Number systems and conversion Binary arithmetic Representation of negative numbers Addition of two s complement numbers Addition of one s complement numbers Binary s Readings Unit.~. UNIT NUMBER

More information

Data Representation. DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.

Data Representation. DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors. Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic ( volts) and one for logic (3.3

More information

Chapter 2: Number Systems

Chapter 2: Number Systems Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This two-valued number system is called binary. As presented earlier, there are many

More information

P( Hit 2nd ) = P( Hit 2nd Miss 1st )P( Miss 1st ) = (1/15)(15/16) = 1/16. P( Hit 3rd ) = (1/14) * P( Miss 2nd and 1st ) = (1/14)(14/15)(15/16) = 1/16

P( Hit 2nd ) = P( Hit 2nd Miss 1st )P( Miss 1st ) = (1/15)(15/16) = 1/16. P( Hit 3rd ) = (1/14) * P( Miss 2nd and 1st ) = (1/14)(14/15)(15/16) = 1/16 CODING and INFORMATION We need encodings for data. How many questions must be asked to be certain where the ball is. (cases: avg, worst, best) P( Hit 1st ) = 1/16 P( Hit 2nd ) = P( Hit 2nd Miss 1st )P(

More information

But first, encode deck of cards. Integer Representation. Two possible representations. Two better representations WELLESLEY CS 240 9/8/15

But first, encode deck of cards. Integer Representation. Two possible representations. Two better representations WELLESLEY CS 240 9/8/15 Integer Representation Representation of integers: unsigned and signed Sign extension Arithmetic and shifting Casting But first, encode deck of cards. cards in suits How do we encode suits, face cards?

More information

Logic, Words, and Integers

Logic, Words, and Integers Computer Science 52 Logic, Words, and Integers 1 Words and Data The basic unit of information in a computer is the bit; it is simply a quantity that takes one of two values, 0 or 1. A sequence of k bits

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

CS 253. January 14, 2017

CS 253. January 14, 2017 CS 253 Department of Computer Science College of Engineering Boise State University January 14, 2017 1/30 Motivation Most programming tasks can be implemented using abstractions (e.g. representing data

More information

Chapter 1. Digital Systems and Binary Numbers

Chapter 1. Digital Systems and Binary Numbers Chapter 1. Digital Systems and Binary Numbers Tong In Oh 1 1.1 Digital Systems Digital age Characteristic of digital system Generality and flexibility Represent and manipulate discrete elements of information

More information

UNIVERSITY OF WISCONSIN MADISON

UNIVERSITY OF WISCONSIN MADISON CS/ECE 252: INTRODUCTION TO COMPUTER ENGINEERING UNIVERSITY OF WISCONSIN MADISON Prof. Gurindar Sohi TAs: Lisa Ossian, Minsub Shin, Sujith Surendran Midterm Examination 1 In Class (50 minutes) Wednesday,

More information

Chapter 4: Data Representations

Chapter 4: Data Representations Chapter 4: Data Representations Integer Representations o unsigned o sign-magnitude o one's complement o two's complement o bias o comparison o sign extension o overflow Character Representations Floating

More information

Math 230 Assembly Programming (AKA Computer Organization) Spring 2008

Math 230 Assembly Programming (AKA Computer Organization) Spring 2008 Math 230 Assembly Programming (AKA Computer Organization) Spring 2008 MIPS Intro II Lect 10 Feb 15, 2008 Adapted from slides developed for: Mary J. Irwin PSU CSE331 Dave Patterson s UCB CS152 M230 L10.1

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

Five classic components

Five classic components CS/COE0447: Computer Organization and Assembly Language Chapter 3 modified by Bruce Childers original slides by Sangyeun Cho Dept. of Computer Science Five classic components I am like a control tower

More information

Register Transfer Language and Microoperations (Part 2)

Register Transfer Language and Microoperations (Part 2) Register Transfer Language and Microoperations (Part 2) Adapted by Dr. Adel Ammar Computer Organization 1 MICROOPERATIONS Computer system microoperations are of four types: Register transfer microoperations

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts

More information

10.1. Unit 10. Signed Representation Systems Binary Arithmetic

10.1. Unit 10. Signed Representation Systems Binary Arithmetic 0. Unit 0 Signed Representation Systems Binary Arithmetic 0.2 BINARY REPRESENTATION SYSTEMS REVIEW 0.3 Interpreting Binary Strings Given a string of s and 0 s, you need to know the representation system

More information

ECE 331: N0. Professor Andrew Mason Michigan State University. Opening Remarks

ECE 331: N0. Professor Andrew Mason Michigan State University. Opening Remarks ECE 331: N0 ECE230 Review Professor Andrew Mason Michigan State University Spring 2013 1.1 Announcements Opening Remarks HW1 due next Mon Labs begin in week 4 No class next-next Mon MLK Day ECE230 Review

More information

Bits, Bytes and Integers

Bits, Bytes and Integers Bits, Bytes and Integers Computer Systems Organization (Spring 2016) CSCI-UA 201, Section 2 Instructor: Joanna Klukowska Slides adapted from Randal E. Bryant and David R. O Hallaron (CMU) Mohamed Zahran

More information

CSC201, SECTION 002, Fall 2000: Homework Assignment #2

CSC201, SECTION 002, Fall 2000: Homework Assignment #2 1 of 7 11/8/2003 7:34 PM CSC201, SECTION 002, Fall 2000: Homework Assignment #2 DUE DATE Monday, October 2, at the start of class. INSTRUCTIONS FOR PREPARATION Neat, in order, answers easy to find. Staple

More information

Multiplies the word length <ea> times the least significant word in Dn. The result is a long word.

Multiplies the word length <ea> times the least significant word in Dn. The result is a long word. MATHEMATICAL INSTRUCTIONS Multiply unsigned MULU ,dn Action Notes: Example: Multiplies the word length times the least significant word in Dn. The result is a long word. 1. The lowest word of

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

8/27/2016. ECE 120: Introduction to Computing. Graphical Illustration of Modular Arithmetic. Representations Must be Unambiguous

8/27/2016. ECE 120: Introduction to Computing. Graphical Illustration of Modular Arithmetic. Representations Must be Unambiguous University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing Signed Integers and 2 s Complement Strategy: Use Common Hardware for Two Representations

More information

l l l l l l l Base 2; each digit is 0 or 1 l Each bit in place i has value 2 i l Binary representation is used in computers

l l l l l l l Base 2; each digit is 0 or 1 l Each bit in place i has value 2 i l Binary representation is used in computers 198:211 Computer Architecture Topics: Lecture 8 (W5) Fall 2012 Data representation 2.1 and 2.2 of the book Floating point 2.4 of the book Computer Architecture What do computers do? Manipulate stored information

More information

17. Instruction Sets: Characteristics and Functions

17. Instruction Sets: Characteristics and Functions 17. Instruction Sets: Characteristics and Functions Chapter 12 Spring 2016 CS430 - Computer Architecture 1 Introduction Section 12.1, 12.2, and 12.3 pp. 406-418 Computer Designer: Machine instruction set

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

Brock Wilcox CS470 Homework Assignment 2

Brock Wilcox CS470 Homework Assignment 2 Brock Wilcox CS470 Homework Assignment 2 Please complete the following exercises from Chapter 2 of Patterson & Hennessy, Computer Organization & Design: The Hardware/Software Interface, Fourth Edition,

More information

Bitwise Instructions

Bitwise Instructions Bitwise Instructions CSE 30: Computer Organization and Systems Programming Dept. of Computer Science and Engineering University of California, San Diego Overview v Bitwise Instructions v Shifts and Rotates

More information

Binary Adders: Half Adders and Full Adders

Binary Adders: Half Adders and Full Adders Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order

More information

SE311: Design of Digital Systems

SE311: Design of Digital Systems SE311: Design of Digital Systems Lecture 3: Complements and Binary arithmetic Dr. Samir Al-Amer (Term 041) SE311_Lec3 (c) 2004 AL-AMER ١ Outlines Complements Signed Numbers Representations Arithmetic Binary

More information

QUIZ ch.1. 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law

QUIZ ch.1. 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law QUIZ ch.1 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law Integrated circuits Density of silicon chips doubles every 1.5 yrs. Multi-core CPU Transistors

More information

8086 Programming. Multiplication Instructions. Multiplication can be performed on signed and unsigned numbers.

8086 Programming. Multiplication Instructions. Multiplication can be performed on signed and unsigned numbers. Multiplication Instructions 8086 Programming Multiplication can be performed on signed and unsigned numbers. MUL IMUL source source x AL source x AX source AX DX AX The source operand can be a memory location

More information

C NUMERIC FORMATS. Overview. IEEE Single-Precision Floating-point Data Format. Figure C-0. Table C-0. Listing C-0.

C NUMERIC FORMATS. Overview. IEEE Single-Precision Floating-point Data Format. Figure C-0. Table C-0. Listing C-0. C NUMERIC FORMATS Figure C-. Table C-. Listing C-. Overview The DSP supports the 32-bit single-precision floating-point data format defined in the IEEE Standard 754/854. In addition, the DSP supports an

More information

Floating Point Considerations

Floating Point Considerations Chapter 6 Floating Point Considerations In the early days of computing, floating point arithmetic capability was found only in mainframes and supercomputers. Although many microprocessors designed in the

More information

Floating-point Arithmetic. where you sum up the integer to the left of the decimal point and the fraction to the right.

Floating-point Arithmetic. where you sum up the integer to the left of the decimal point and the fraction to the right. Floating-point Arithmetic Reading: pp. 312-328 Floating-Point Representation Non-scientific floating point numbers: A non-integer can be represented as: 2 4 2 3 2 2 2 1 2 0.2-1 2-2 2-3 2-4 where you sum

More information

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1 IT 1204 Section 2.0 Data Representation and Arithmetic 2009, University of Colombo School of Computing 1 What is Analog and Digital The interpretation of an analog signal would correspond to a signal whose

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

Numbers and Representations

Numbers and Representations Çetin Kaya Koç http://koclab.cs.ucsb.edu/teaching/cs192 koc@cs.ucsb.edu Çetin Kaya Koç http://koclab.cs.ucsb.edu Fall 2016 1 / 38 Outline Computational Thinking Representations of integers Binary and decimal

More information

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:

More information

Microcomputers. Outline. Number Systems and Digital Logic Review

Microcomputers. Outline. Number Systems and Digital Logic Review Microcomputers Number Systems and Digital Logic Review Lecture 1-1 Outline Number systems and formats Common number systems Base Conversion Integer representation Signed integer representation Binary coded

More information

Computer Arithmetic. L. Liu Department of Computer Science, ETH Zürich Fall semester, Reconfigurable Computing Systems ( L) Fall 2012

Computer Arithmetic. L. Liu Department of Computer Science, ETH Zürich Fall semester, Reconfigurable Computing Systems ( L) Fall 2012 Reconfigurable Computing Systems (252-2210-00L) all 2012 Computer Arithmetic L. Liu Department of Computer Science, ETH Zürich all semester, 2012 Source: ixed-point arithmetic slides come from Prof. Jarmo

More information

Bits, Bytes, and Integers Part 2

Bits, Bytes, and Integers Part 2 Bits, Bytes, and Integers Part 2 15-213: Introduction to Computer Systems 3 rd Lecture, Jan. 23, 2018 Instructors: Franz Franchetti, Seth Copen Goldstein, Brian Railing 1 First Assignment: Data Lab Due:

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

Floating Point Arithmetic

Floating Point Arithmetic Floating Point Arithmetic CS 365 Floating-Point What can be represented in N bits? Unsigned 0 to 2 N 2s Complement -2 N-1 to 2 N-1-1 But, what about? very large numbers? 9,349,398,989,787,762,244,859,087,678

More information

Lecture 9. INC and DEC. INC/DEC Examples ADD. Arithmetic Operations Overflow Multiply and Divide

Lecture 9. INC and DEC. INC/DEC Examples ADD. Arithmetic Operations Overflow Multiply and Divide Lecture 9 INC and DEC Arithmetic Operations Overflow Multiply and Divide INC adds one to a single operand DEC decrements one from a single operand INC destination DEC destination where destination can

More information

15110 Principles of Computing, Carnegie Mellon University - CORTINA. Digital Data

15110 Principles of Computing, Carnegie Mellon University - CORTINA. Digital Data UNIT 7A Data Representa1on: Numbers and Text 1 Digital Data 10010101011110101010110101001110 What does this binary sequence represent? It could be: an integer a floa1ng point number text encoded with ASCII

More information

Learning the Binary System

Learning the Binary System Learning the Binary System www.brainlubeonline.com/counting_on_binary/ Formated to L A TEX: /25/22 Abstract This is a document on the base-2 abstract numerical system, or Binary system. This is a VERY

More information

CS/ECE 252: INTRODUCTION TO COMPUTER ENGINEERING UNIVERSITY OF WISCONSIN MADISON

CS/ECE 252: INTRODUCTION TO COMPUTER ENGINEERING UNIVERSITY OF WISCONSIN MADISON CS/ECE 252: INTRODUCTION TO COMPUTER ENGINEERING UNIVERSITY OF WISCONSIN MADISON Prof. Gurindar Sohi, Kai Zhao TAs: Annie Lin, Mohit Verma, Neha Mittal, Daniel Griffin, Yuzhe Ma Examination 1 In Class

More information

1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM

1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1.1 Introduction Given that digital logic and memory devices are based on two electrical states (on and off), it is natural to use a number

More information

Introduction To MIPS Assembly Language Programming

Introduction To MIPS Assembly Language Programming Gettysburg College Open Educational Resources 2015 Introduction To MIPS Assembly Language Programming Charles W. Kann Gettysburg College Follow this and additional works at: http://cupola.gettysburg.edu/oer

More information

2.2 THE MARIE Instruction Set Architecture

2.2 THE MARIE Instruction Set Architecture 2.2 THE MARIE Instruction Set Architecture MARIE has a very simple, yet powerful, instruction set. The instruction set architecture (ISA) of a machine specifies the instructions that the computer can perform

More information

Characters, Strings, and Floats

Characters, Strings, and Floats Characters, Strings, and Floats CS 350: Computer Organization & Assembler Language Programming 9/6: pp.8,9; 9/28: Activity Q.6 A. Why? We need to represent textual characters in addition to numbers. Floating-point

More information

CHAPTER 4: Register Transfer Language and Microoperations

CHAPTER 4: Register Transfer Language and Microoperations CS 224: Computer Organization S.KHABET CHAPTER 4: Register Transfer Language and Microoperations Outline Register Transfer Language Register Transfer Bus and Memory Transfers Arithmetic Microoperations

More information

Declaring Floating Point Data

Declaring Floating Point Data Declaring Floating Point Data There are three ways to declare floating point storage. These are E D L Single precision floating point, Double precision floating point, and Extended precision floating point.

More information

H.1 Introduction H-2 H.2 Basic Techniques of Integer Arithmetic H-2 H.3 Floating Point H-13 H.4 Floating-Point Multiplication H-17 H.

H.1 Introduction H-2 H.2 Basic Techniques of Integer Arithmetic H-2 H.3 Floating Point H-13 H.4 Floating-Point Multiplication H-17 H. H.1 Introduction H-2 H.2 Basic Techniques of Integer rithmetic H-2 H.3 Floating Point H-13 H.4 Floating-Point Multiplication H-17 H.5 Floating-Point ddition H-21 H.6 Division and Remainder H-27 H.7 More

More information

CS367 Test 1 Review Guide

CS367 Test 1 Review Guide CS367 Test 1 Review Guide This guide tries to revisit what topics we've covered, and also to briefly suggest/hint at types of questions that might show up on the test. Anything on slides, assigned reading,

More information

Introduction to Computer Science. Homework 1

Introduction to Computer Science. Homework 1 Introduction to Computer Science Homework. In each circuit below, the rectangles represent the same type of gate. Based on the input and output information given, identify whether the gate involved is

More information

Chapter (1) Eng. Mai Z. Alyazji

Chapter (1) Eng. Mai Z. Alyazji THE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DIGITAL LOGIC DESIGN DISCUSSION ECOM 2012 Chapter (1) Eng. Mai Z. Alyazji September, 2016 1.1 List the octal and hexadecimal

More information