ABSTRACT
This chapter discusses the various aspects of the data processing unit of a CPU (central processing unit), the ALU (arithmetic and logic unit). The different types of number systems, their numerical representations, and the relationships with one another, including the representation of decimal fixed-point and floating-point numbers in the binary system with normalized form and related IEEE standards, universally followed by all ALUs, have been described. Floating-point arithmetic operations (addition and subtraction) of signed numbers with overflow consideration have been shown with examples. The basic structure of an ALU with the required hardware elements, and the different types of basic adders and subtracters as well as the design principle and implementation of high-speed adders used in practice have been illustrated with appropriate figures and related worked-out example. Booth’s algorithm for fast multiplication of signed and unsigned numbers and its machine implementation have been depicted with the respective figure. Different methods for division of signed and unsigned numbers using the machine-based algorithms have been shown.
