LOGIC CIRCUIT

LOGIC GATES
A logic gate is an elementary building block of a digital circuit. It processes one or more input signal in a logical fashion. Depending on the input value or voltage, the logic gate will either output a value of ‘1’ for ON or a value of ‘0’ for OFF.
BINARY CODE
Logic gates are digital circuits and they utilize a binary numbering system known as binary code. Binary code is the same language used by computer which uses only 1 or 0 as numbers.
INPUTS AND OUTPUTS
Gates have two or more inputs, except a NOT gate which has only one input. All gates have only one output. Usually the letters A, B, C and so on are used to label inputs and output.

LOGIC SYMBOL OF THE “AND” GATE
HOW DOES THE AND GATE WORK?
‘AND’ gates are like two or more switches in series. All the switches have to be closed (ON or value of 1) in order to make the lamp (output) turn on. If all the inputs are not ‘ON’, the output is ‘OFF’.
TRUTH TABLE FOR “AND” GATE

INPUT
INPUT
OUTPUT
A
B
C
0
0
0
0
1
0
1
0
0
1
1
1


All the value of the AND gate must be a ‘1’ in order or the output value to be ‘1’. Any other input combination will result in zero.
OR GATE
An ‘OR’ gate is like two or more switches in series. Only one switch need to be closed (ON or value of 1) in order to make the lamp (output C) turn ON with a value of 1.

LOGIC SYMBOL FOR “OR” GATE
TRUTH TABLE OF “OR” GATE

INPUT
INPUT
OUTPUT
A
B
C
0
0
0
0
1
1
1
0
1
1
1
1
A value of ‘1’ applied to either or both inputs of the OR gate will result in an output value of ‘1’. A value of ‘0’ applied to both inputs will result in an output of ‘0’.

NOT GATE
NOT gate have only one input and output. It reverses the input signal value. If the input is 1, the output will be 0 and if the input is 0 then the output will be 1.
LOGIC SYMBOL FOR “NOT” GATE
TRUTH TABLE FOR “NOT” GATE

INPUT
OUTPUT
A
C
0
1
1
0
“NOT” gate can be referred as inverter, whatever the input signal is the output is always the opposite.

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.
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 = A
A complement bar is placed over the assigned input letter. The expression is read as X is equal A which simply means that the output state is opposite of the logic state applied to the input.
 

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