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3 BOOLEAN LOGIC
Chapter Outline
3.1 Realising Binary Signals 3.2 Binary Logic
3.3 Boolean Algebra 3.4 Boolean Algebra for Logic Circuits
Introduction
Digital computers are based on discrete information elements, called digital signals or logic signals. As these signals
assume only two values, they are also called binary signals. The two values of a binary signal may be called 1-0,
true-false, high-low, etc.
3.1 Realising Binary Signals
Electrical quantities such as voltage and current are used to denote binary signals. For example, a high voltage, say,
5.0, may be used to denote logic signal 1 and a low voltage, say, 0, may be used to denote a logic signal 0. As it is
difficult to achieve exact values (0 and 5) of voltage, some variations from these ideal values are allowed. For example,
a particular system may interpret voltage in the range 0.0 to 0.5 as logic 0 and voltage in the range 4.0 to 5.0 as logic
1. The voltage values between 0.5 and 4.0 may be considered erroneous.
3.2 Binary Logic
Binary logic deals with operations on binary data. It is used to design electronic circuits for digital computers. It uses
three basic operations: two binary operations AND and OR, and a unary operation NOT. In the following discussion, we
shall use A, B, C, x, y, etc., to denote binary variables and 1-0 to denote the two binary constants. Sometimes,
we may use true-false in place of 1-0.
3.2.1 AND Operator
The AND operator (often called AND gate) is denoted by writing AND, putting a dot, or simply by the absence of an
operator. Thus, A AND B, A ● B, and AB all mean the same. The value of A AND B is defined to be 1 if both A and B are
1 and 0; otherwise, as shown in Table 3.1.
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