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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