Combinational Circuit

COMBINATIONAL CIRCUITS

• Logic circuit formed by combinational of logic circuit. Logic gates are connected together to produce a specified output
• Various combinations of input values can determine the combinational logic circuit’s output
• Boolean algebra provides a concise way to express the operation of combinational logic circuit

It can be defined in three way :

1.  Truth table – A truth table shows how a logic circuit's output responds to various combinations of the inputs, using logic 1 for true and logic 0 for false

Example:

Table 2.2.1: Example Of truth table

2.  Graphical symbols- The layout of connected gates that represent the logic gates.

Example:

Table 2.2.2 : Sample of logic circuit

3.  Boolean equation – A combinational logic circuit can be described by a Boolean equation

Can be represented in two forms :

    i. SOP ( Sum Of Product ) – 

       •  When two or more product terms are summed by Boolean addition. 

    ii. POS (Product Of Sum )

       •  When two or more product terms are multiplied by Boolean multiplication. 

Two ways to simplify Boolean equation

    i.  Laws of Boolean algebra – A set of rules for symbolic manipulation are needed in order to simplify Boolean expression.

Table 2.2.3 Basic Law of Boolean Algebra

Example : 

 Table 2.2.3.1 Simplify Boolean Algebra

ii.  Karnaugh Map (K-Map) – Comprise a box / grid for every line in the truth table.

• Straight forward method of minimizing Boolean expression.
• The diagram below illustrates the correspondence between K-Map and the truth table for the general case of two variables.

Table 2.2.4 : Mintermsand K-Map for 3 variable

DeMorgan’s Law

• DeMorgan’s theorems provide mathematical verification of the equivalency of the NAND,NOR

Table : DeMorgan’s Law Logic Gates

Published by :

Syaqira Liyana Binti Ahmad Ghazali 

( B031310568 )