SS 2 WEEK FIVE LESSON NOTE

TOPIC: Logic Circuits

Introduction

A logic gate is the fundamental building block of digital integrated circuits. Most logic gate takes an input of two binary values, and output a single value of 1 or 0. Some circuits may have only a few logic gates, while others, such as microprocessors, may have millions of them. Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tube, fluidic logic, optics, molecules or even mechanical elements.


Logic circuit includes such devices as registers, arithmetic logic units, and computer memory, all the way up through complete microprocessors, which may contain more than 100 million gates.  

Types of logic circuit

There are mainly 3 logic gates, they are:
·           OR gate
·           AND gate
·           NOT gate

Equation and truth table for each logic gate

The truth table is the table that shows the possible combinations of variable values in the equation and the result (output) for each of the logic gates.
For a two-input truth table, there will be 4 (22) possible combinations of variable inputs and generally for n-input truth table, there will be 2n possible combinations of the input variables. See the examples below:

1.    OR gate: 
The OR gate is a circuit that has two or more inputs and operates in such a way that:
·         Its output is 1 when any of the input variables is 1
·         Its output is 0 if when all of the input variables are 0
·         Its output is 1 when all of the input variables are 0
The algebraic symbol of the OR operation is the plus sign (+).

The OR gate is represented graphically below.






The OR gate is represented in a truth table (with two inputs A and B) as shown below:

A
B
X=A + B
0
0
0
0
1
1
1
0
1
1
1
1

        It can also be generated using the equation: X=A+B

2.    AND gate: 
The AND gate is a circuit that has two or more inputs and operates in such a way that:
·         Its output is 1 if and only if the two inputs are 1
·         Its output is 0 if any of the inputs is either 0 or 1 or both are 0

The algebraic symbol of the AND gate is * or .. The AND gate is represented graphically below.



     

    
The AND gate is represented in a truth table (with two inputs A and B) as shown below:

A
B
X=A * B
0
0
0
0
1
0
1
0
0
1
1
1

It can also be generated using the equation: X=A.B

3.    NOT gate: 
This is the logic gate that has one input and one output such that when the input is true (1), the output is false and when the input is false, the output is true.

The algebraic symbol of the NOT gate is     or ‘. The NOT gate is represented graphically below.

The truth table for the NOT gate (with input A): x= A’ or x= ážš is shown below:

A
X = A’
0
1
1
0


Assignment :

An OR gate has 3 inputs and 1 output. Show the truth table for this OR gate.




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