8.2.4 Binary Multiplication
One of the biggest and slowest circuits in an arithmetic and logic unit is the multiplier. We'll start by developing a straightforward implementation and then, in the next section, look into tradeoffs to make it either smaller or faster. Here's the multiplication operation for two unsigned 4-bit operands broken down into its component operations. This is exactly how we learned to do it in primary school. We take each digit of the multiplier (the B operand) and use our memorized multiplication tables to multiply it with each digit of the multiplicand (the A operand), dealing with any carries into the next column as we process the multiplicand right-to-left. The output from this step is called a partial product and then we repeat the step for the remaining bits of the multiplier. Each partial product is shifted one digit to the left, reflecting the increasing weight of the multiplier digits. In our case the digits are just single bits, i.e., they're 0 or 1 and t...