Chapter 3, Problem 3.16E

Program Plan Intro

Booth’s Algorithm:

In order to multiply two signed binary numbers in 2’s complement format, Booth algorithm is used.

Steps in Booth Algorithm:

First one needs to assign the multiplicand as “BR” and multiplier as “QR”. Then the algorithm works as per the following conditions:

• If “$Q_n$” and “$Q_{n+1}$ are same which is “00” or “11”, then one needs to perform arithmetic shift by 1 bit.
•  If “$Q_n$” and “$Q_{n+1}$”= “10”, then one needs to do “$A=A+BR$” and perform arithmetic shift by 1 bit.
•  If “$Q_n$” and “$Q_{n+1}$”= “01”, then one needs to do “A= A – BR” and perform arithmetic shift by 1 bit.

Adder:

In Electronics, an Adder is a digital circuit that performs addition of numbers.