Computer Architecture

Lecture 15Fasih ur Rehman

Last Class

• Arithmetic– Representation– Signed numbers– Operations and their implementation

Today’s Agenda

• Arithmetic operations

Overflow (Examples)

Overflow

• Overflow in case of addition can only occur when both the operands have same sign.

• Condition for Overflow• Overflow happens when (at MSB)

Carry in ≠ Carry out• Normally, overflow is referred to ‘V’ flag in status

register

Addition/subtraction of signed numbers

si =ci +1 =

13

7+ Y

1

00010

1

1

00110

11

0

01101001

0

0

0

0

1

1

1

1

00001111

Example:

10= = 0

01 1

11 1 0 0

1

1 1 10

Legend for stage i

xi yi Carry-in ci Sum s i Carry-out ci+1

X

Z

+ 6 0+xiyisi

Carry-outci+1

Carry-inci

xiyicixiyicixiyicixiyici x i yi ciÅ Å=+ + +

yicixicixiyi+ +

Logic for Single Stage

n – bit Ripple Carry Adder

Cascade for k n – bit Adders

Summary

• Overflow• Addition• Adders