5 Arithmetic for Computers PART1

8/17/2019 5 Arithmetic for Computers PART1

1/12

Lecture 5


2/12

Page 2 2

Binary Number System

In any number base, the value of ith

digit d is, d x Basei

where i starts at 0 & increases from right to left

For eg, 1011 ! "1x#$ % "0x$ % "1x1$ % "1x0$ ! 1110

I'S word is # bits long, hence we can re(resent #)bit (atterns

*east Significant Bit "*SB$ + efers to the rightmost bit "bit 0$

ost Significant Bit "SB$ + efers to the leftmost bit "bit #1$


3/12

Page 3 3

-ddition & Subtraction

.g 1/ 10 % 10 230000 0111 ! 10

+ 230000 0110 ! 10

230000 1101 ! 1#10

.g / 10 ) 10

230000 0111 ! 10

) 231111 1010 ! )10

230000 0001 ! 110


4/12

Page 4 4

ulti(lication

ulti(ly 1000 by 1001

First o(erand, 1000 + ulti(licand

Second o(erand, 1001+ ulti(lier

'roduct + 1001000

For an n)bit multi(licand & m)bit multi(lier, (roduct is 4 m%n bits


5/12

Page 5 5

ulti(lication 5ardware


6/12

Page 6 6

ulti(lication -lgorithm


7/12

Page 7 7

efined 6ersion of ulti(lication 5ardware


8/12

Page 8 8

ulti(lication -lgorithm


9/12

Page 9 9

ulti(lication in I'S

I'S has two #)bit registers to contain the 7)bit (roduct/ 5i& *o

I'S instructions for multi(lication/ mult "multi(ly$ & multu

"multi(ly unsigned$

8 mult 9s, 9s# : 'laces 7)bit (roduct in 5i*o

;o move the (roduct to general (ur(ose registers I'S uses twoinstructions/ mflo "move from *o$ & mfhi "move from 5i$

8 mfhi 9s1 :9s1 ! 5i


10/12

Page 10 10


11/12

Page 11 11


12/12

Page 12 12

5 Arithmetic for Computers PART1

Documents

Transcript of 5 Arithmetic for Computers PART1