Subject :- VLSI Design

Topic :- MOS Circuit Design Styles

Difficulty :- Medium

• Multiplication is a mathematical operation that at its simplest is an abbreviated process of adding an integer to itself a specified number of times. The operation of multiplication is rather simple in digital electronics. It has its origin from the classical algorithm for the product of two binary numbers.

• This algorithm uses addition and shift left operations to calculate the product of two numbers .Based upon the above procedure, we can deduce an algorithm for any kind of multiplication. We can check at the initial stage also that whether the product will be positive or negative or after getting the whole result, MSB of the results tells the sign of the product. Digital multiplication is a series of bit shifts and bit additions, where two numbers, the multiplicand and the multiplier are combined into the result.

• Considering the bit representations of the multiplicand $X_0\,X_1 \,X_2……X_{n-1}$ and the multiplier $Y_0\,Y_1\,Y_2….Y_{n-1}$, in order to form the product, up to n shifted copies of the multiplicand is to be added for unsigned multiplication.

• The entire process consists of three steps, partial product generation, partial product reduction and final addition. Digital multiplication consists of three basic steps, these are:-

1. Generation of Partial Product Array
2. Reduction of Partial Product Array
3. Final addition.