Performing Logical Calculations
Logical Calculations are performed with Boolean Algebra. Variables in logical calculations have only two values, True and False. Truth is represented by a “1” and False is represented by a “0”.
For Octal or Hexadecimal calculations,
the values are converted to Octal or Hexadecimal.
Type of logical calculations and truth tables
AND: Product of propositions
Produces 1 when all input values are 1.
OR Sum of propositions
Produces 1 when one or more input values are 1.
XOR Exclusive Sum of propositions
Produces 0 when all input values are either 1 or 0. (Other cases acts as an OR)
XNOR Exclusive sum of propositions
Combination of XOR and NOT
NOT Negation
Produces the opposite value of the Input.
Examples:
1100 | AND | 1010 | = | (1000.) |
1100 | OR | 1010 | = | (1110.) |
1100 | XOR | 1010 | = | (110) |
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Truth Tables |
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AND | INPUT |
| OUTPUT |
A | B |
| X |
1 | 1 |
| 1 |
1 | 0 |
| 0 |
0 | 1 |
| 0 |
0 | 0 |
| 0 |
OR | INPUT |
| OUTPUT |
A | B |
| X |
1 | 1 |
| 1 |
1 | 0 |
| 1 |
0 | 1 |
| 1 |
0 | 0 |
| 0 |
XOR, XNOR | INPUT |
| OUTPUT |
A | B | X OR X NOR | |
1 | 1 | 0 | 1 |
1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 |
NOT | INPUT |
| OUTPUT |
A | X |
1 | 0 |
0 | 1 |
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