15.01.2013 Views

U. Glaeser

U. Glaeser

U. Glaeser

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Array Multipliers<br />

An alternative approach to multiplication involves the combinational generation of all bit products and<br />

their summation with an array of full adders. The block diagram of a 6 by 6 array multiplier is shown<br />

in Fig. 9.10. It uses a 6 by 6 array of cells to form the bit products and five adders (at the bottom of the<br />

array) to complete the evaluation of the product. Three types of cells are used in the square array: gate cells<br />

(marked G in Fig. 9.10), which use a single gate to form the logic AND of the x and y inputs to the<br />

cell; half adder cells (marked HA), which sum the second input to the cell with the logic AND of the x<br />

© 2002 by CRC Press LLC<br />

TABLE 9.3 Radix-4 Modified Booth Multiplication<br />

a i+1 a i a i −1 Operation<br />

0 0 0 P = P/4<br />

0 0 1 P = (P + B)/4<br />

0 1 0 P = (P + B)/4<br />

0 1 1 P = (P + 2 B)/4<br />

1 0 0 P = (P – 2 B)/4<br />

1 0 1 P = (P – B)/4<br />

1 1 0 P = (P – B)/4<br />

1 1 1 P = P/4<br />

POSITIVE TIMES POSITIVE A = 5<br />

i aiai-1 = 0.101<br />

8<br />

OPERATION<br />

3<br />

B = 4 = 0.110<br />

RESULT<br />

0 1 0 P = (P – B)/2 1.1010<br />

1 0 1 P = (P + B)/2 0.00110<br />

2 1 0 P = (P – B)/2 1.101110<br />

3 0 1 P = P + B<br />

THUS: P = 0.011110 =<br />

0.011110<br />

15<br />

32<br />

NEGATIVE TIMES POSITIVE A = – 5<br />

i aiai-1 8 = 1.011<br />

OPERATION<br />

3<br />

B = = 0.110<br />

4<br />

RESULT<br />

0 1 0 P = (P – B)/2 1.1010<br />

1 1 1 P = P/2 1.11010<br />

2 0 1 P = (P + B)/2 0.010010<br />

3 1 0 P = P – B<br />

THUS: P = 1.100010 = –<br />

1.100010<br />

15<br />

32<br />

POSITIVE TIMES NEGATIVE A = 5<br />

8 = 0.101 B = – 3<br />

4 = 1.010<br />

i aiai-1 OPERATION RESULT<br />

0 1 0 P = (P – B)/2 0.0110<br />

1 0 1 P = (P + B)/2 1.1010<br />

2 1 0 P = (P – B)/2 0.010010<br />

3 0 1 P = P + B<br />

THUS: P = 1.100010 = –<br />

1.100010<br />

15<br />

32<br />

NEGATIVE TIMES NEGATIVE A = – 5<br />

8 = 1.011 B = – 3<br />

4 = 1.010<br />

i aiai-1 OPERATION RESULT<br />

0 1 0 P = (P – B)/2 0.0110<br />

1 1 1 P = P/2 0.00110<br />

2 0 1 P = (P + B)/2 1.101110<br />

3 1 0 P = P – B<br />

THUS: P = 0.011110 =<br />

0.011110<br />

15<br />

32<br />

FIGURE 9.9 Example of sequential booth multiplication.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!