Digital Logic

Logic gates is an electronic circuit that combines digital signal according to Boolean algebra. The gate also controls the flow of information.

Boolean Algebra 

• uses variables and operators to describes logic circuits.
• Boolean constant and variables are allowed to have only one possible values, 0 and 1.
• The complement of a variable is shown by a bar over the letter.
• If a given variables is 1, the complement of the variables is 0.

Logic Gates and Circuits
Boolean logic provides the foundation for computers and other modern digital electronics. Digital logic circuits are one particular application of boolean logic that uses voltage values to represent true and false, or 1 and 0, if you prefer.
Boolean logic simulators can simulate electronic logic gates in an interactive environment on  computer. Such environments are often used to design circuits before implementing them with real electronic components.

Logic gates

Digital systems are said to be constructed by using logic gates. These gates are the AND, OR, NOT, NAND, NOR, and EXOR gates. The basic operations are described below with the aid of truth tables.

AND gate

The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high.  A dot (.) is used to show the AND operation i.e. A.B.  Bear in mind that this dot is sometimes omitted i.e. AB

OR gate

The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high.  A plus (+) is used to show the OR operation.

 

NOT gate

The NOT gate is an electronic circuit that produces an inverted version of the input at its output.  It is also known as an inverter.  If the input variable is A, the inverted output is known as NOT A.  This is also shown as A', or A with a bar over the top, as shown at the outputs. The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate. It can also be done using NOR logic gates in the same way.

NAND gate

This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate.  The outputs of all NAND gates are high if any of the inputs are low. The symbol is an AND gate with a small circle on the output. The small circle represents inversion.

NOR gate

This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate.  The outputs of all NOR gates are low if any of the inputs are high.

The symbol is an OR gate with a small circle on the output. The small circle represents inversion.

EXOR gate

The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high.  An encircled plus sign () is used to show the EOR operation.

prepared by: nabilah binti shamsur azam (B031310218)

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BOOLEAN EQUATION FORMS

All Boolean equation can be represented in two forms:

• Sum-of-products(SOP)

             - combinations of input values that produce 1 

             - SOP is much easier

• Product-of-sums( P O S)

             - combinations of input values that produces 0s 

             - usually use when 1s  produce is more than 0s 

SIMPLIFICATION OF BOOLEAN EQUATION

There are 2 ways to simplify the boolean equation.

1. LAWS OF BOOLEAN ALGEBRA- using rules to simplify Boolean expression
2. KARNAUGH  MAP - a grid-like representation  of a truth table.

example:

F = A'B' + ABC'D

•   the truth table: