Design a multicycle 4bit multiplier with sequential circuit

Design a multi-cycle 4-bit multiplier with sequential circuit using shifters, adders, DFFs, and gates of your choice. At time point zero, the unsigned 4-bit binary number A and B are provided to you, and your multiplier should calculate the 8-bit product after 4 clock cycles.

Solution

Binary multiplication is similar to normal multiplication.

Note that the product of two 4-bit numbers is potentially an 8-bit number.

eg: Multiplicand -1011

Multiplier -0110

0000

10110

101100

0000000

Product

1000010.

We also need somewhere to store the product.

We can use registers or flip-flops.

Registers will allow us to hold the value as long as we like.

Sometimes, we add zero, sometimes we add a shifted version of the multiplicand.

This suggests AND gates will be needed.

The shift registers are to be used to shift the multiplicand.

For 4-bit multiplication, we need 8-bit shift register.