**LOGIC EQUATIONS**
Aside representing the functioning of a logic gate with truth table and grammatical definition, the use of logic equations can be used not only to represent logic gates and circuits, but also with the usage of some theorems and equivalences, to reduce the number of terms involved, simplifying the equation. In logic equation all Boolean variable involved is assigned a letter or symbol, very similar to the algebraic representation of unknown numerical values using letters. This approach is called Boolean algebra.
**Symbolic logic uses values, variables and operations;**
TRUE is represented as 1
while FALSE as 0.
Variables are represented by letters and can have one or two values, either 0 or 1. Operations are functions of one or more variables.
**AND gate equation**
The AND gate operation can also be expressed by a Boolean algebraic equation. For 2 – input AND gate, the equation is;
X = A.B
The symbol for AND gate operation is a center dot. It does not mean multiplication. The equation read X equals to A and B, which simply mean that the output of the gate is a logic 1 when A and B inputs are in their 1 states.
**OR gate equation**
The Boolean algebraic equation expression is given as;
X = A + B
The equation read X equals to A or B, which simply mean that the output of the gate is a logic 1 when A or B inputs are in their 1 states.
**NOT gate equation**
The NOT gate operation can be expressed by a Boolean algebraic equation as;
X = Ᾱ
A complement bar is placed over the assigned input letter. The expression is read as X is equal Ᾱ which simply means that the output state is opposite of the logic state applied to the input.
**USES OF LOGIC GATES**
Logic gates are in fact the building block of digital electronics, they are formed by the combination of transistors to realise some digital operations (Like Logical OR, AND, NOT). Every digital product like computers, mobile, calculators even digital watches contains logic gates. The use of logic gates can be understood by the following example: the single bit full adder in digital electronics is a logic circuit which perform the logical addition of two single bit binary numbers. |