4 - Computer arithmetic

Abstract

A result of choosing to represent numbers in binary notation is that logic circuits can be devised to process the numbers. This chapter describes the process of designing a simple adder circuit, which is then developed into a more useful arithmetic and logic unit (ALU). The chapter demonstrates how the simple adder can be made to operate faster by using the carry-look-ahead technique. Finally, it looks at how floating-point numbers are represented and how arithmetic is performed on them. Large computers usually incorporate a hardware floating-point unit (FPU), which performs the arithmetic operations according to the IEE 754 standard. These FPUs also compute square roots and functions such as sin(), cos(), and log(). To use floating point in a small computer without an FPU, one has to write the program code to perform the operations. A computing machine can then be designed using the concepts and digital devices.