Boolean Algebra

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  • Created by: harryc418
  • Created on: 12-05-17 11:48

Introduction

Computers use boolean logic. Boolean values consist of either 1's and 0's or true and false.

There are 6 boolean laws that can help with simplifying boolean equasions:

  • Commutative law

  • Associative law

  • Distributive law

  • AND law

  • OR law

  • Inversion law

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Commutative Law

Commutative law is when you simply swap the boolean values.

For example:

A.B = B.A          A+B = B+A

Commutative Law states that changing the order of the values does not effect the outcome of the logic circuit.

Proof:

1 OR 0 = 1

0 OR 1 = 1

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Associative law

Associative law is when you change the order of the operations.

For example:

A.(B.C) = (A.B).C = (A.C).B                  A+(B+C) = (A+B)+C = (A+C)+B

Changing the order of the opperation has no impact on the outcome of the logic circuit.

Proof:

(1+2)+3 = 6

(1+3)+2 = 6

(3+2)+1 = 6

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Distributive law

Distributive law is when you expand the brackets.

For example:

A.(B+C) = A.B + A.C

Expanding the brakets has no impact on the outcome of the logic circuit

Proof:

1x(2+3) = 5

1x2+1x3 = 5

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AND law

AND law is composed of combinations of variables to allow you to simplfy faster. Here are the combinations:

A.0 = 0

A.1 = A

A.A = A

A.(NOT A) = 0

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OR law

OR law is composed of combinations of variables to allow you to simplfy faster. Here are the combinations:

A+0 = A

A+A = A

A+1 = 1

A+(NOT A) = 0

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Inversion law

Inversion law only applys when you come across a double NOT opperation. If there is a double NOT opperation then they cancel out.

For example:

NOT(NOT A) = A

Proof:

NOT(NOT 1) = NOT(0) = 1

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A +(not A)=1

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