Design a sequential circuit to multiply an 8-4-2-1

Chapter 16, Problem 16.22

(choose chapter or problem)

Design a sequential circuit to multiply an 8-4-2-1 binary-coded decimal digit by 3 to give a 5-bit binary number. For example, if the input is 0111, the output should be 10101. The input and output to the circuit should be serial with the least significant bit first. Assume that the input will be 0 at the fifth clock time and reset the circuit after the fifth output bit. (Hint: As each bit is received, multiply it by 3, giving a product of either 00 or 11. Thus we either output 0 and carry 0 to the next column, or output 1 and carry 1 to the next column. If we carry a 1 to the next column, then the sum of the carry and the next product is either 01 or 100. In this case, we either output 1 and carry 0 or output 0 and carry 10 (2) to the next column. What happens if we carry 10 (2) to the next column?)

(a) Derive a state table with a minimum number of states (3 states).

(b) Design the circuit using J-K flip-flops and NAND and NOR gates.

(c) Design the circuit using a PLA and D flip-flops. Give the PLA table.