Booth’s Multiplication Algorithm

Booth's algorithm is a multiplication algorithm that multiplies two signed binary numbers in 2's complement notation. 
Booth used desk calculators that were faster at shifting than adding and created the algorithm to increase their speed. Booth’s algorithm is of interest in the study of computer architecture. Here's the implementation of the algorithm. 
Examples: 
 

Input : 0110, 0010
Output : qn q[n+1] AC QR sc(step count)
 initial 0000 0010 4
 0 0 rightShift 0000 0001 3
 1 0 A = A - BR 1010
 rightShift 1101 0000 2
 0 1 A = A + BR 0011
 rightShift 0001 1000 1
 0 0 rightShift 0000 1100 0

Result=1100

 

Algorithm : 
 

Put multiplicand in BR and multiplier in QR 
and then the algorithm works as per the following conditions : 
1. If Q_n and Q_n+1 are same i.e. 00 or 11 perform arithmetic shift by 1 bit. 
2. If Q_n Q_n+1 = 01 do A= A + BR and perform arithmetic shift by 1 bit. 
3. If Q_n Q_n+1 = 10 do A= A - BR and perform arithmetic shift by 1 bit. 
 

 

Output : 
 

qn q[n + 1] BR AC QR sc
 initial 0000 1010 4
0 0 rightShift 0000 0101 3
1 0 A = A - BR 1010
 rightShift 1101 0010 2
0 1 A = A + BR 0011
 rightShift 0001 1001 1
1 0 A = A - BR 1011
 rightShift 1101 1100 0

Result = 1100

Time Complexity: O(n)

 Auxiliary Space: O(1)