Question

2. Show the trace of the RTL code for Booth's algorithm for X = 0111 and Y = 1011.

Answer 1

Solution:

Booth's Multiplication for X= 0111 , Y =1011 is shown below:

Booths algorithm check the values of Q₀Q_-1 ?

If Q₀Q_-1 =00 or 11 Do Just Arithmetic Right Shift(ARS) of A,Q Q₀

If Q₀Q_-1 =10 Do A <- A - M then Just Arithmetic Right Shift(ARS) of A,Q Q₀

If Q₀Q_-1 =01 Do A <- A + M then Just Arithmetic Right Shift(ARS) of A,Q Q₀

_{Here A is Accumulator, Q is Multiplier , M is Multiplicand, Q0 is LSB of Q and Q-1 is next digit to Q0}

_{Here x =0111 ( Multiplicand)}

_{Y=1011 ( Multiplier)}

Step Count 'n'	A	Q	Q-1	M	Description
4	0000	1011	0	0111	Intialised
4 3	1001 1100	1011 1101	0 1	0111 0111	Step-1, Compare Q0Q-1 =10 So A = A-M then ASR A Q Q0 then decrement 'n'
2	1110	0110	1	0111	Step-2, Compare Q0Q-1 =11 So Only ASR A Q Q0 then decrement 'n'
2 1	1110 0101 0010	0110 0110 1011	1 1 0	0111 0111 0111	Step :3 As Q0Q-1 =01, Then A <- A + M and ASR A Q Q-1, decrement count 'n
1 0	1011 1101	1011 1101	0 1	0111 0111	Step 4: Check Q0Q-1= 10 so A = A - M then ASR A,Q Q-1 then less the count by one