**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.

**B****oolean 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

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