TABLE OF CONTENTS Various information-processing jobs are carried out by digital computers. Arithmetic operations are among the basic functions of a digital computer. Addition of two binary digits is the most basic arithmetic operation. The simple addition consists of four possible elementary operations, which are 0+0 = 0, 0+1 = 1, 1+0 = 1, and 1+1 = 10. The first three operations produce a sum of one digit, but the fourth operation produces a sum consisting of two digits. The higher significant bit of this result is called the carry. A combinational circuit that performs the addition of two bits as described above is called a half-adder. When the augend and addend numbers contain more significant digits, the carry obtained from the addition of two bits is added to the next higher-order pair of significant bits. Here the addition operation involves three bits the augend bit, addend bit, and the carry bit and produces a sum result as well as carry. The combinational circuit performing this type of addition operation is called a full-adder. In circuit development two half-adders can be employed to form a full-adder.
As described above, a half-adder has two inputs and two outputs. Let the input variables augend and addend be designated as A and B, and output functions be designated as S for sum and C for carry. The truth table for the functions is below.
From the truth table in Figure 5.2, it can be seen that the...
