Question

Multiply 14 times -5 using 5-bit numbers?

Fill in the table for the Product, Multiplier and Multiplicand for each step.

You need to provide the DESCRIPTION of the step being performed.

Answer 1

The flowchart of booth's multiplication algorithm for unsigned number is as follows:-

According to the question multiplicand = 14, multiplier = -5

Now using the above flow chart the initial values of the registers are as follows:-

BR = 14 => 5 bit binary representation of BR = 01110

5 bit binary representation of (BR' + 1) = 10010

QR = -5 => 5 bit binary representation of QR = 11011

SC = number of bits in BR/QR => SC = 5 = 101.

Q0Q-1	Operation	AC	QR	Q-1	SC
		00000	11011	0	101
10	AC <- AC+BR'+1 ASHR ACQRQ-1	10010 11001	11011 01101	0 1	100
11	ASHR ACQRQ-1	11100	10110	1	011
01	AC <- AC+BR ASHR ACQRQ-1	01010 00101	10110 01011	1 0	010
10	AC <- AC+BR'+1 ASHR ACQRQ-1	10111 11011	01011 10101	0 1	001
11	ASHR ACQRQ-1	11101	11010	1	000

Since the value of SC becomes 0 therefore we stop the further processing, the final product/ result will be the binary value of ACQR which is (1110111010)₂ which is 2's compliment of 70 (that is -70) and hence it is equivalent to decimal value -70, it shows that the answer is correct as 14*-5 will be equal to -70.