Multiply 14 times -5 using 5-bit numbers? Fill in the table for the Product, Multiplier and...

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.

Solutions

Expert Solution

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.

venereology answered 2 years ago

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