University of California, Santa Barbara: Behrooz Parhami's "Multiplication"
Study slides 1-26. In particular, focus on section 9.1 to learn how multiplication is performed using basic steps that are carried out by elemental logic components, such as an adder and shifter. Two numbers are loaded into registers (fast word storage) and multiplication is carried out by repeated addition and shifting (moving the bits in a register to the right or left). The presentation first shows how multiplication is done for unsigned integers and then how signed numbers are handled.
When you read the slides, follow along by using a pad of paper and multiply two small binary numbers. Note k is the position of the binary digit; from right to left, k takes on 0, 1, 2, etc. j is the partial product; j goes from 1, 2, 3, etc. However, for consistency the 0th partial product is defined to be 0. Chapters 10-12 are optional; these chapters discuss ways of speeding up multiplication.
Note that to multiply two floating point numbers, add the exponents, multiply the mantissas, normalize the mantissa of the product, and adjust the exponent accordingly. Floating point multiplication will be covered in a following subunit 4.4.