Computer Systems Lecture 8 Multiplication, Division, and - PowerPoint PPT Presentation

CS 230 – Introduction to Computers and Computer Systems Lecture 8 – Multiplication, Division, and Conditional Execution CS 230 - Spring 2020 2-1

Multiplication and Division special locations hi and lo mult $s, $t  multiply registers s and t  place result in hi : lo  in CS230 we can ignore hi for multiplication only div $s, $t  divide register s by t  place integer quotient in lo , remainder in hi  hi is very useful here CS 230 - Spring 2020 2-2

Multiplication and Division Results mfhi $d  copy contents of hi to register d mflo $d  copy contents of lo to register d CS 230 - Spring 2020 2-3

Example addi $2, $0, -3 mult $2, $2 mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-4

Example addi $2, $0, -3 mult $2, $2 $0 $1 $2 $3 $4 $5 … ? … mflo $3 0 ? ? ? ? jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-5

Example addi $2, $0, -3 mult $2, $2 $0 $1 $2 $3 $4 $5 … ? … mflo $3 0 ? -3 ? ? jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-6

Example addi $2, $0, -3 lo = 9 mult $2, $2 $0 $1 $2 $3 $4 $5 … ? … mflo $3 0 ? -3 ? ? jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-7

Example addi $2, $0, -3 lo = 9 mult $2, $2 $0 $1 $2 $3 $4 $5 … ? … mflo $3 0 ? -3 9 ? jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-8

Example addi $2, $0, -3 lo = 9 mult $2, $2 $0 $1 $2 $3 $4 $5 … ? … mflo $3 0 ? -3 9 ? jr $31 What is the value in register $3 at the end of this program? • $3 = 9 10 CS 230 - Spring 2020 2-9

Try it Yourself addi $2, $0, 11 addi $4, $0, 5 div $2, $4 mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-10

Try it Yourself addi $2, $0, 11 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? ? ? ? mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-11

Try it Yourself addi $2, $0, 11 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? 11 ? ? mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-12

Try it Yourself addi $2, $0, 11 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? 11 ? 5 mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-13

Try it Yourself addi $2, $0, 11 hi = 1 lo = 2 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? 11 ? 5 mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-14

Try it Yourself addi $2, $0, 11 hi = 1 lo = 2 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? 11 2 5 mflo $3 jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-15

Try it Yourself addi $2, $0, 11 hi = 1 lo = 2 addi $4, $0, 5 $0 $1 $2 $3 $4 $5 … ? … div $2, $4 0 ? 11 2 5 mflo $3 jr $31 What is the value in register $3 at the end of this program? • $3 = 2 10 CS 230 - Spring 2020 2-16

Conditional Execution  Computation dependent on intermediate results  otherwise only linear number crunching CS 230 - Spring 2020 2-17

Conditional Branch beq $s, $t, i  compare registers s and t  if equal , skip i instructions  i can be negative bne $s, $t, i  compare registers s and t  if not equal , skip i instructions  i can be negative CS 230 - Spring 2020 2-18

Branch Labels  Use a label instead of i  leave computation of i to the assembler (binasm)  example label here called loop addi $1, $0, 10 loop: addi $1, $1, -1 bne $1, $0, loop jr $31  in branch instructions we can write loop instead of -2  binasm will turn bne $1, $0, loop into bne $1, $0, -2 CS 230 - Spring 2020 2-19

Program Counter (PC)  MIPS word size is 32-bits  therefore each instruction is 32-bits = 4 bytes long  Program counter = address of current instruction  the dashed line from examples  we’ll talk more about addresses later  always incremented by 4 at each instruction  since instructions are 4 bytes, this moves to next instruction  beq and bne do PC=PC+( i *4) when condition met CS 230 - Spring 2019 2-20

Example addi $2, $0, 10 addi $3, $0, 0 x: add $3, $3, $2 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-21

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? ? ? ? PC = 0x54 addi $2, $2, -1 (we don’t know the value of PC here, but lets pretend for this bne $2, $0, x example that it starts at 0x54) jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-22

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 10 ? ? PC = 0x58 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-23

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 10 0 ? PC = 0x5C addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-24

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 10 10 ? PC = 0x60 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-25

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 9 10 ? PC = 0x64 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-26

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 9 10 ? PC = 0x5C addi $2, $2, -1 PC = 0x64 + 4 10 + (4 10 * -3 10 ) bne $2, $0, x (-3) jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-27

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 9 19 ? PC = 0x60 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-28

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 8 19 ? PC = 0x64 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-29

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 8 19 ? PC = 0x5C addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-30

Example - Skip to $2=1 addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 1 55 ? PC = 0x60 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-31

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 0 55 ? PC = 0x64 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-32

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 0 55 ? PC = 0x68 addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-33

Example addi $2, $0, 10 addi $3, $0, 0 $0 $1 $2 $3 $4 $5 … ? … x: add $3, $3, $2 0 ? 0 55 ? PC = 0x6C addi $2, $2, -1 bne $2, $0, x jr $31 What is the value in register $3 at the end of this program? $3 = 55 10 CS 230 - Spring 2020 2-34

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 beq $3, $0, tt addi $3, $0, 37 tt: jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-35

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 $0 $1 $2 $3 $4 $5 … ? … beq $3, $0, tt 0 ? ? ? ? PC = ? + 0 10 addi $3, $0, 37 tt: jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-36

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 $0 $1 $2 $3 $4 $5 … ? … beq $3, $0, tt 0 ? ? 10 ? PC = ? + 4 10 addi $3, $0, 37 tt: jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-37

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 $0 $1 $2 $3 $4 $5 … ? … beq $3, $0, tt 0 ? ? 0 ? PC = ? + 8 10 addi $3, $0, 37 tt: jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-38

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 $0 $1 $2 $3 $4 $5 … ? … beq $3, $0, tt 0 ? ? 0 ? (1) PC = ? + 16 10 addi $3, $0, 37 PC = (? + 8 10 ) + 4 10 + (4 10 * 1 10 ) tt: jr $31 What is the value in register $3 at the end of this program? CS 230 - Spring 2020 2-39

Try it Yourself addi $3, $0, 10 sub $3, $3, $3 $0 $1 $2 $3 $4 $5 … ? … beq $3, $0, tt 0 ? ? 0 ? PC = ? + 20 10 addi $3, $0, 37 tt: jr $31 What is the value in register $3 at the end of this program? • $3 = 0 10 CS 230 - Spring 2020 2-40