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Computer Arithmetic

Introduction

Algorithm – solution to any problem that is stated

by a finite number of well-defined procedural

steps.

Algorithms for addition, subtraction,

multiplication and division

Fixed point binary data in signed magnitude

representation

Fixed point binary data in signed 2’s complement

representation

Floating point binary data

Addition and Subtraction of signed

magnitude numbers

Hardware for signed magnitude

addition and subtraction

B Register

Complementer

Parallel adder

A Register

B

S

AVF

E

Output

carry

A

S

S

Input carry

M (Mode Control)

Load Sum

Problems

Mark each individual path in the flow chart by a

number and then indicate the overall path that

the algorithm takes when the following signed

magnitude numbers are computed. In each case

give the value of AVF. The left most bit in the

following numbers represents the sign bit

Signed magnitude addition

1 1 1 1 1

E = AVF = 1

Problems

Perform the arithmetic operations below with

binary numbers and with negative numbers in

signed 2’s complement representation. Use

seven bits to accommodate each number

together with its sign. In each case, determine if

there is an overflow by checking the carries into

and out of the sign bit position