A Binary multiplier is an electronic hardware device used in digital electronics or a computer or other electronic device to perform rapid multiplication of two numbers in binary representation. It is built using binary adders

The basic implementation of a Binary Multiplier is to: 1. AND each of the bits of the Multiplicand (defined as B0, B1, B2, for all the bits that you have) with the first bit of the multiplier (A0). A0 AND B0 becomes the first bit of the output - C0 2. AND each of the bits of the Multiplicand with the next bit of the Multiplier. 3. Add these using a Binary Adder to the remaining bits from the previous group AND ( {B0, B1, B2, ...} AND {A0} in this case). The least significant bit from the adder becomes C1, the next output bit. 4. Repeat step 2 and 3 until all bits of the Multiplier are used. The Carry from the last adder becomes the final bit in the product. 5.

Example:

2 Bit by 2 Bit Binary Multiplier
Using a 4 Bit + 4 Bit Adder

WARNING: THIS IMAGE IS INCORRECT! B VALUES ON THE SECOND AND THIRD 4-BIT ADDERS ARE INCORRECTLY ANDED.

4 Bit by 4 Bit Binary Multiplier
Using 4 Bit + 4 Bit Adders