Question

Consider the following 8-bit multiplication problem: 0110 1100 x 0011 1001

For count the number of additions (and/or subtractions) for the basic binary multiplication show in figure 10.9 and for Booth's algorithm shown in figure 10.12. What is the 16 bit product?

START C,A-0 M-Multiplicand Multiplier Count- Flowchart for Unsigned Binary Multiplication No C,A-A+M Shift right C,A, Q Count Count- No Yes_ END Product in A,Q Figure 10.9 Flowchart for Unsigned Binary Multiplication

Answer 1

C, A rightarrow 0 m = 01101100 Q = 00111001 Count = n = 8 Q_0 = 1 C, A Rightarrow 01101100 (A + m) Addition = 1 C, A, Q = 00110110 Shift right Count = Count - 1 = 8 - 1 = 7 Q_0 = 1 No rightarrow Shift Right C, A, Q Count = Count - 1 = 7 - 1 = 6 C, A, Q = 0 0 0 1 1 0 11 = 0 No - Again Check q_0 = 1 yes = C, A = A + M C, A = 10000111 downarrow Right shift downarrow C/A = 0100011 Q = 00001101 m - A = 00011011 + M = 0 1101100/10000111 Addition = 2 count - = 6 + = 5 \r\n Count = 0? No go to Q_o = 1 ? - yes C, A leftarrow A + m = 01000011 01101100 10101111 Addition = 3 Shift Right C, A, Q downarrow Q = 00000110 C, A
16 bit multiplication is:0001011110001100