Admin CS41B MACHINE. Midterm topics. Admin 2/11/16. Midterm next Thursday in-class (2/18) SML. recursion. math. David Kauchak CS 52 Spring 2016

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1 Admin! Assignment 3! due Monday at :59pm! Academic honesty CS4B MACHINE David Kauchak CS 5 Spring 6 Admin Midterm next Thursday in-class (/8)! Comprehensive! Closed books, notes, computers, etc.! Except, may bring up to pages of notes! Practice problems posted # Also some practice problems in the Intro SML reading! Midterm review sessions (will announce on piazza soon) Midterm topics SML recursion math

2 Midterm topics Binary number revisited! Basic syntax! SML built-in types! Defining function! pattern matching! Function type signatures! Recursion!! map! exceptions! Defining datatypes! addition, subtraction, multiplication manually and on list digits! Numbers in different bases! Binary number representation (first part of today s lecture)! NOT CS4B material What number does represent in binary? Depends! Is it a signed number or? If signed, what convention are we using? Twos complement Twos complement For a number with n digits high order bit represents - n- What number is it? signed (twos complement) - 3 signed (twos complement) - 3-7

3 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? 6 ( 4 ) numbers,,,., Doesn t matter the representation! Twos complement How many numbers can we represent with each approach using 3 bits? 3 4 billion numbers 3 3 signed (twos complement) - 3 signed (twos complement) - 3 3

4 Twos complement What is the range of numbers we can represent for each approach with 4 bits? :,, 5 signed: -8, -7,, 7 signed (twos complement) 3-3 binary representation? binary representation twos complement? binary representation twos complement ?

5 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! 5

6 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 ( $ and $ )! Add! 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 ( $ and $ )! Add! Resulting number is the magnitude of the original negative number flip the bits add -3 flip the bits add - Addition with twos complement numbers Addition with twos complement numbers +? + 6

7 Addition with twos complement numbers Addition with twos complement numbers +? +? Addition with twos complement numbers Addition with twos complement numbers +? 6 5 +? Overflow! We cannot represent this number (it s too large) 7

8 Addition with twos complement numbers Addition with twos complement numbers + ignore the last carry Subtraction Subtraction! Negate the nd number (flip the bits and add )! Add them! Ideas? 8

9 Hexadecimal numbers Hexadecimal = base 6 What will be the digits? Hexadecimal numbers Hexadecimal = base 6 Digits 9 a () b () c () d (3) e (4) f (5) What number is ad? Hexadecimal numbers Hexadecimal = base 6 Digits Hexadecimal numbers Hexadecimal = base 6 Digits 9 a () b () c () d (3) e (4) f (5) a d = 56+*6+3= = a () b () c () d (3) e (4) f (5) Hexadecimal is common in CS. Why? 9

10 Hexadecimal numbers Hexadecimal = base 6 Digits Hexadecimal numbers Hexadecimal = base 6 Digits 9 a () b () c () d (3) e (4) f (5) Hexadecimal is common in CS. 4 bits = hexadecimal digit What is the following number in hex? 9 a () b () c () d (3) e (4) f (5) Hexadecimal is common in CS. 4 bits = hexadecimal digit What is the following number in hex? 6 d 5 Computer internals Computer internals simplified CPU What does it stand for? What does it do? What does it stand for? What does it do?

11 Computer internals simplified Computer internals simplified the computer CPU (Central Processing Unit, aka the processor ) (Random Access Memory, aka memory or main memory ) CPU hard drive Does all the work! Temporary storage Why do we need a hard drive? Computer internals simplified Computer simplified the computer hard drive the computer CPU hard drive CPU network - Persistent memory - only stores data while it has power input devices display media drive

12 Inside the CPU Memory speed CPU processor registers processor: does the work registers: local, fast memory slots operation access time times slower than register access register.3 ns s ns 4 6 min for comparison Hard disk ms ~million month google.com.4s ~billion 3 years Why all these levels of memory? Memory Memory What is a byte?? byte = 8 bits byte is abbreviated as B My laptop has 6GB (gigabytes) of memory. How many bits is that?

13 Memory sizes Memory sizes bits byte 8 kilobyte (KB) ^ bytes = ~8, megabyte (MB) ^ =~ 8 million gigabyte (GB) ^3 = ~8 billion bits byte 8 kilobyte (KB) ^ bytes = ~8, megabyte (MB) ^ =~ 8 million gigabyte (GB) ^3 = ~8 billion My laptop has 6GB (gigabytes) of memory. How many bits is that? ~8 billion bits! Memory Memory address address 3 3 Memory is byte addressable Memory is organized into words, which is the most common functional unit 3

14 Memory Memory in the CS4B Machine address 3-bit words address 6-bit words Most modern computers use 3-bit (4 byte) or 64-bit (8 byte) words We ll use 6-bit words for our model (the CS4B machine) CS4B machine CS4B instructions CPU processor ic instruction counter (location in memory of the next instruction in memory) CPU processor r r holds the value (read only) What types of operations might we want to do (think really basic)? r - general purpose - read/write registers r3 registers 4

15 operation name (always three characters) operation arguments R = register (e.g. r) S = signed number (byte) operation function dest = first register src = second register src = third register arg = number/argument 5

16 add r r r3 What does this do? add r r r3 r = r + r3 Add contents of registers r and r3 and store the result in r adc r r What does this do? adc r r r = r + Add to the contents of register r and store in r 6

17 adc r r 8 neg r r sub r r r adc r r 8 neg r r sub r r r r = 8 r = -8, r = 8 r = 6 What number is in r? 7