TABLE OF CONTENTS Objective: Humans are used to doing arithmetic operations with decimal numbers, while computers perform similar arithmetic operations but use the binary system of 0 s and 1 s. The objective of this chapter is to show how the latter occurs. The analysis includes unsigned and signed values, of both integer and real-valued types. Because shift operations can also implement certain arithmetic functions, they too are included in this chapter.
Chapter Contents
| 3.1 | Unsigned Addition |
| 3.2 | Signed Addition and Subtraction |
| 3.3 | Shift Operations |
| 3.4 | Unsigned Multiplication |
| 3.5 | Signed Multiplication |
| 3.6 | Unsigned Division |
| 3.7 | Signed Division |
| 3.8 | Floating-Point Addition and Subtraction |
| 3.9 | Floating-Point Multiplication |
| 3.10 | Floating-Point Division |
| 3.11 | Exercises |
Binary addition (also called modulo-2 addition) was introduced in Section 2.5, with Figure 2.5 repeated in Figure 3.1 below. The vectors within the gray area are given, while the others must be calculated. a = a 3 a 2 a 1 a 0 and b = b 3 b 2 b 1 b 0 represent 4-bit numbers to be added, producing a 5-bit sum vector, sum = s 4 s 3 s 2 s 1 s 0, and a 4-bit carry vector, carry = c 4 c 3 c 2 c 1. The algorithm is summarized in (b) (recall that it is a modulo-2 operation). In (c), an example is given in which "1100" (= 12) is added to "0110" (= 6), producing "10010" (= 18)...
