Admin. ! Assignment 3. ! due Monday at 11:59pm! one small error in 5b (fast division) that s been fixed. ! Midterm next Thursday in-class (10/1)

Transcription

1 Admin CS4B MACHINE David Kauchak CS 5 Fall 5! Assignment 3! due Monday at :59pm! one small error in 5b (fast division) that s been fixed! Midterm next Thursday in-class (/)! 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 Tuesday and Wednesday (Q&A session for midterm) Midterm topics SML recursion math Midterm topics! 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

2 Binary number revisited Twos complement What number does represent in binary? Depends! Is it a signed number or? If signed, what convention are we using? For a number with n digits high order bit represents - n- signed (twos complement) 3-3 Twos complement Twos complement What number is it? What number is it? signed (twos complement) signed (twos complement) - 3 -

3 Twos complement What number is it? Twos complement How many numbers can we represent with each approach using 4 bits? 3 6 ( 4 ) numbers,,,., Doesn t matter the representation! signed (twos complement) signed (twos complement) 3-3 Twos complement How many numbers can we represent with each approach using 3 bits? 3 4 billion numbers Twos complement What is the range of numbers we can represent for each approach? :,, 5 signed: -8, -7,, signed (twos complement) - 3 signed (twos complement) - 3 3

4 binary representation? binary representation twos complement? binary representation twos complement ? binary representation twos complement ?

5 binary representation twos complement binary representation twos complement How can you tell if a number is negative? binary representation twos complement High order bit! 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 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 flip the bits add - Addition with twos complement numbers +? Addition with twos complement numbers Addition with twos complement numbers + +? 6

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

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

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

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. Why? 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? Hexadecimal numbers Computer internals 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? 6 d 5

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

12 Computer simplified Inside the CPU the computer hard drive CPU CPU processor processor: does the work network registers: local, fast memory slots media drive registers input devices display Why all these levels of memory? Memory speed Memory 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 What is a byte??

13 Memory Memory sizes bits byte 8 kilobyte (KB) ^ bytes = ~8, megabyte (MB) ^ =~ 8 million gigabyte (GB) ^3 = ~8 billion byte = 8 bits byte is abbreviated as B My laptop has 6GB (gigabytes) of memory. How many bits is that? My laptop has 6GB (gigabytes) of memory. How many bits is that? Memory sizes Memory bits byte 8 kilobyte (KB) ^ bytes = ~8, megabyte (MB) ^ =~ 8 million gigabyte (GB) ^3 = ~8 billion address 3 ~8 billion bits! Memory is byte addressable 3

14 Memory Memory address address 3-bit words Memory is organized into words, which is the most common functional unit Most modern computers use 3-bit (4 byte) or 64-bit (8 byte) words Memory in the CS4B Machine CS4B machine address bit words CPU processor ic r instruction counter (location in memory of the next instruction in memory) holds the value (read only) r We ll use 6-bit words for our model (the CS4B machine) registers r r3 - general purpose - read/write 4

15 CS4B instructions CPU processor What types of operations might we want to do (think really basic)? registers operation name (always three characters) operation arguments R = register (e.g. r) S = signed number (byte) 5

16 add r r r3 What does this do? operation function dest = first register src = second register src = third register arg = number/argument 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? 6

17 adc r r r = r + Add to the contents of register r and store in r adc r r 8 neg r r sub r r r What number is in r? adc r r 8 neg r r sub r r r r = 8 r = -8, r = 8 r = 6 7