Digital Systems

Chapter 3

Binary Arithmetic and Two’s Complement Arithmetic

OBJECTIVE

In Chapter 2, we learnt binary numbers. We used unsigned (positive) numbers only. In this chapter, the concept of binary arithmetic numbers (positive and negative) and their operations will be discussed. We shall also learn the concept of two’s complement numbers and their operations.

A 32-bit computer system, like a Pentium, can easily perform arithmetic operations on two binary numbers as big as four bytes (32 bits) [1 byte = 8 bits]. Nowadays, computers can simultaneously deal with an 8-byte word (a 64-bit number).

3.1 BINARY ADDITION ARITHMETIC

Let us assume that two arithmetic number A and B each of four bits, which are to be added. Let us assume bits in A are A₃