February 22, 2018

Truth-Tables, Boolean Equations

What Is a Truth Table?

A Truth Table lists all possible input combinations for a logic circuit and the corresponding output for each combination. It's used to visualise and analyze logic gates and expressions.

Example: 2-input AND Gate

A

B

Output (A AND B)

0

0

0

0

1

0

1

0

0

1

1

1

Boolean Equations

Boolean Equations represent logic operations mathematically, using symbols like:

+ → OR

· → AND

¬ or ' → NOT

Common Logic Functions

Operation

Symbol

Equation Example

Output Rule

AND

·

A · B

Output is 1 only if both are 1

OR

+

A + B

Output is 1 if either is 1

NOT

¬ or '

¬A or A'

Output is 1 if A is 0

XOR

A B

Output is 1 if inputs differ

Example: Boolean Equation to Truth Table

Let’s take a logic expression: Y = A · B + ¬C

A

B

C

¬C

A·B

Y (A·B + ¬C)

0

0

0

1

0

1

0

0

1

0

0

0

0

1

0

1

0

1

0

1

1

0

0

0

1

0

0

1

0

1

1

0

1

0

0

0

1

1

0

1

1

1

1

1

1

0

1

1

 

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