Concept Flow - Logical operators (and, or, xor, not, nand, nor)
Input A, Input B
Output Result
Use in Circuit or Simulation
Logical operators take two inputs (except not) and produce an output based on the operator's rule.
0
0
Logical operators (and, or, xor, not, nand, nor) in VHDL - Step-by-Step Execution
Execution Sample
VHDL
library ieee; use ieee.std_logic_1164.all; signal A, B, Result_and, Result_or : std_logic; Result_and <= A and B; Result_or <= A or B;
This code shows how to use 'and' and 'or' logical operators on signals A and B.
Execution Table
| Step | A | B | A and B | A or B | A xor B | not A | A nand B | A nor B |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
| 3 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 4 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| Exit | - | - | - | - | - | - | - | All input combinations tested |
💡 All input combinations of A and B (0 or 1) are tested to show operator outputs.
Variable Tracker
| Variable | Start | After 1 | After 2 | After 3 | After 4 | Final |
|---|---|---|---|---|---|---|
| A | - | 0 | 0 | 1 | 1 | 1 |
| B | - | 0 | 1 | 0 | 1 | 1 |
| A and B | - | 0 | 0 | 0 | 1 | 1 |
| A or B | - | 0 | 1 | 1 | 1 | 1 |
| A xor B | - | 0 | 1 | 1 | 0 | 0 |
| not A | - | 1 | 1 | 0 | 0 | 0 |
| A nand B | - | 1 | 1 | 1 | 0 | 0 |
| A nor B | - | 1 | 0 | 0 | 0 | 0 |
Key Moments - 3 Insights
Why does 'not A' invert only A and not B?
'not' is a unary operator, so it only takes one input. See execution_table rows where 'not A' flips A's value only.
What is the difference between 'and' and 'nand'?
'nand' is the inverse of 'and'. When 'and' is 1, 'nand' is 0, and vice versa. Check rows 4 for example.
Why is 'xor' 0 when both inputs are the same?
'xor' outputs 1 only when inputs differ. When both are 0 or 1, 'xor' is 0. See rows 1 and 4.
Visual Quiz - 3 Questions
Test your understanding
Look at the execution_table at Step 3, what is the value of 'A or B'?
💡 Hint
Check the 'A or B' column in execution_table row with Step 3.
At which step does 'A nand B' become 0?
💡 Hint
Look at 'A nand B' column in execution_table and find where value is 0.
If A changes from 0 to 1 at Step 3, how does 'not A' change?
💡 Hint
Refer to 'not A' values in variable_tracker from After 1 to After 3.
Concept Snapshot
Logical operators in VHDL: - and, or, xor: binary operators on two inputs - not: unary operator on one input - nand, nor: inverse of and, or - Outputs are std_logic values (0 or 1) - Used to build digital logic circuits
Full Transcript
This visual execution shows how logical operators in VHDL work step-by-step. Inputs A and B take all combinations of 0 and 1. For each, the operators and, or, xor, not, nand, and nor produce outputs. 'not' only flips A because it is unary. 'nand' and 'nor' invert 'and' and 'or' results. The execution table tracks each operator's output for every input pair. Variable tracker shows how each signal changes over steps. Key moments clarify common confusions like unary vs binary operators and operator inverses. The quiz tests understanding by asking about specific steps and values. This helps beginners see exactly how logical operators behave in VHDL.