Combinational Multipliers do multiplication of two unsigned binary numbers. Each bit of the

multiplier is multiplied against the multiplicand, the product is aligned according to the position of the bit within

the multiplier, and the resulting products are then summed to form the final result. Main advantage of binary

multiplication is that the generation of intermediate products are simple: if the multiplier bit is a $1,$ the product is

an appropriately shifted copy of the multiplicand; if the multiplier bit is a $0,$ the product is simply $0.$

Theory:

The design of a combinational multiplier to multiply two $4-$bit binary number is illustrated below:

A$3$ A$2$ A$1$ A$0$

B$3$ B$2$ B$1$ B$0$

A$3.$ B$0$ A$2.$ B$0$ A$1.$ B$0$ A$0.$ B$0$

A$3.$ B$1$ A$2.$ B$1$ A$1.$ B$1$ A$0.$ B$1$

A$3.$ B$2$ A$2.$ B$2$ A$1.$ B$2$ A$0.$ B$2$

A$3.$ B$3$ A$2.$ B$3$ A$1.$ B$3$ A$0.$ B$3$

S$6$ S$5$ S$4$ S$3$ S$2$ S$1$ S$0$