Multiplication of binary numbers is performed in the same way as with decimal numbers.
The multiplicand is multiplied by each bit of the multiplier, starting from the least significant bit.
The result of each such multiplication forms a partial product. Successive partial products are shifted one bit to the left.
The product is obtained by adding these shifted partial products.
Consider an example of multiplication of two numbers, say A and B (2 bits each), C = A x B.
The first partial product is formed by multiplying the B1B0 by A0. The multiplication of two bits such as A0 and B0 produces a 1 if both bits are 1; otherwise it produces a 0 like an AND operation. So the partial products can be implemented with AND gates.