Digital Logic

Basic of Logic Gates (Part 1)

Logic Circuit

• Perform operations on digital signal
  - implemented as electronic circuits where signal value are restricted to a few discrete value.
• There are only two values 0 and 1. 

Logic Signal

There are a number of different systems for representing binary information in physical systems.

• Foundation for digital computer.
• Boolean Algebra uses variables and operators to represent logic circuits.
• Variables and function have only one value, 0 and 1. The complement of variable is shown such as A'.

Table below shows the Basic Logic Gates

Basic Logic Gates

Description of Logic Gates with Truth Table

Combinational Circuits

• Made up from basic logic NAND, NOR, NOT gates that combined or connected together.
• Converts the binary code data present at its input into a number of different output lines.
• Combinational Circuits can be defined in three ways :
• Truth Table => many possible combinations of input values, in tabular form between input values and the result of specific Boolean operator.
• Graphycal Symbol => layout of connected gates that represent the logic circuit.
• Boolean Equation => Boolean function that consist possible combination of inputs that produce an output signals.

Example 1 : Combination Circuit

Example 2 : Combination Circuit

Boolean Equation (Part 2)

• Most practical use in the simplification of logic circuits.
• Very useful in Boolean simplification, and for the most part bear similarity to many identities and properties.
• Combination of variables and operators.
• Typically has one or more inputs and produces an output in the range of 0 and 1.

Boolean Equation can be represented in two forms:

• Sum-of-product (SOP)


• combination of inputs values that produce 1s is convert into equivalent variables, ANDed together then ORed with other combination variables with same output.
• easier to derive from truth table.

  

  Example : Sum-of-product 

  
  
• Product-of-sum (POS)


• input combination that produce 0 in sum terms, ORed variable are ANDed together.
• convert input values that produce 0s into equivalent variables, ORed the variables and then ANDed with other ORed forms.
• usually use if more 1s produce in output function.
  

  

  Example : Product-of-sum

  
  
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