DIGITAL LOGIC (Boolean Algebra and Logic Gates) by Cheah Siew Kwan

Basic of  Logic Gates

The Boolean algebra can represent the logic gates.Boolean algebra operator can be explain by using truth table.

The truth table for Boolean algebra :                                                                               

AND Truth Table

OR Truth Table

NOT Truth Table

XOR Truth Table

 Boolean algebra variables(in mathematical system) can only have

one value,0 and1.

To show the logical circuit we can use graphical symbol to understand it.

Combination Circuits

Simple combination circuit:

Boolean Equation

Boolean equation can be represent in two form:

1. Sum of Product (SOP)

example:

F=A’B+ABC

Therefore, F=A’BC+A’BC’+ABC

2. Product of Sum (POS)

example

F=(A+C)(A’+B’+C)(B)

pic

Therefore, F=(A'+B'+C)+(A'+B+C')+(A'+B+C)+(A+B'+C)+(A+B+C')+(A+B+C)

Laws of Boolean Algebra

Boolean expression can be simplify and manipulate by using the basic laws to help you manipulating Boolean Algebra equation.

1. Identity Law

    AND form: A(1)=A

    OR form: A+0=A

2. Zero and One Law

    AND form: A(0)=0

    OR form: A+1=1

3. Inverse Law

   AND form: A(A’)=0

   OR form: A+A’=1

4. Idempotent Law

   AND form: A(A)=A

   OR form: A+A=A

5.Commutative Law

   AND form: A(B)=B(A)

   OR form: A+B=B+A

6.Associative Law

   AND form: A(BC)=(AB)C

   OR form: A+(B+C)=(A+B)+C

7.Distributive Law

  AND form: A+(B(C))=(A+B)(A+C)

  OR form: A(B+C)=AB+AC

8.Absorption Law

   AND form: A(A+B)=A

   OR form: A+(AB)=A

                  A+(A’B)=A+B

9.DeMorgan’s Law

   AND form: (A’B’)=A’+B’

   OR form: (A’+B’)=A’(B’)