Page 84 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 5: Combinational Circuits

on the other hand, are quite economical for low-volume production and rapid prototyping, but Notes
may not yield the best performance, density, or power consumption.
Simplification is the process of choosing the least costly implementation from among feasible and
equivalent implementations with the targeted technology.

5.1 Adder

In electronics, an adder is a digital circuit that performs addition of binary numbers. In modern
computers adders reside in the arithmetic logic unit (ALU).

Adders are important not only in computers but also in many types of digital systems in which
the numeric data are processed.

There are two types of adders:
• Half adder
• Full adder
5.1.1 Half Adder

The half adder is an example of a simple, functional digital circuit built from two logic gates. The
half adder adds to one-bit binary numbers (AB). The output is the sum of the two bits (S) and
the carry (C). Note how the same two inputs are directed to two different gates. The inputs to
the XOR gate are also the inputs to the AND gate. The input “wires” to the XOR gate are tied to
the input wires of the AND gate; thus, when voltage is applied to the A input of the XOR gate,
the A input to the AND gate receives the same voltage.

Figure 5.1: (a) Logic Diagram of Half Adder (b) Truth Table of Half Adder

(a)

A B S C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
(b)

5.1.2 Full Adder

The full-adder circuit adds three one-bit binary numbers (C A B) and outputs two one-bit binary
numbers, a sum (S) and a carry (C1). The full adder is usually a component in a cascade of adders,
which add 8, 16, 32, etc. binary numbers. The carry input for the full-adder circuit is from the
carry output from the circuit “above” itself in the cascade. The carry output from the full adder
is fed to another full adder “below” itself in the cascade. If you look closely, you will see the full
adder is simply two half adders joined by an OR.

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