Binary Logic
The three core operations — AND, OR, NOT — that combine true/false values.
Description
A two-valued (0/1) logic with operations AND, OR, and NOT. It is the mathematical model that hardware logic gates physically implement. Define each operation by a truth table; combine them to express any decision.
- AND (·): true only when all operands are true.
- OR (+): true when at least one operand is true.
- NOT (′): flips the value.
- Each operation maps to a gate that produces the corresponding voltage.
- Truth tables fully specify behavior for every input combination.
- What: A two-valued (0/1) logic with operations AND, OR, and NOT.
- Why: It is the mathematical model that hardware logic gates physically implement.
- How: Define each operation by a truth table; combine them to express any decision.
- Where: Every combinational circuit and the algebra used to design it.
- When: From the very first step of specifying what a circuit should do.
At a glance
What
A two-valued (0/1) logic with operations AND, OR, and NOT.
Why
It is the mathematical model that hardware logic gates physically implement.
How
Define each operation by a truth table; combine them to express any decision.
Where
Every combinational circuit and the algebra used to design it.
When
From the very first step of specifying what a circuit should do.
Think of it like…
Like club entry rules: AND = 'need BOTH ticket and ID', OR = 'either one will do', NOT = 'flip the rule'. Combine these three and you can express any entry policy.
The three operations
- AND (·): true only when all operands are true.
- OR (+): true when at least one operand is true.
- NOT (′): flips the value.
Logic ↔ hardware
- Each operation maps to a gate that produces the corresponding voltage.
- Truth tables fully specify behavior for every input combination.
AND / OR / NOT
| A | B | A·B | A+B | A′ |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 |
AND / OR / NOT and friends
▶ live simulatorClick a terminal (A/B) to toggle it · glowing wires carry a logic 1 · the lamp is output Y
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The 5 Whys
- 1
Why binary logic? To reason precisely about two-valued signals.
- 2
Why only three operations? AND, OR, NOT are functionally complete.
- 3
Why does completeness matter? Any function can be built from them.
- 4
Why map to gates? So the logic runs physically in silicon.
- 5
Root cause: a tiny complete operation set bridges human intent and hardware behavior.
Cheat sheet
Working principle
- Define each operation by a truth table; combine them to express any decision.
- A two-valued (0/1) logic with operations AND, OR, and NOT.
Formulas & Boolean expressions
- NOT (′): flips the value.
Key facts
- AND (·): true only when all operands are true.
- Each operation maps to a gate that produces the corresponding voltage.
Why it exists
- Root cause: a tiny complete operation set bridges human intent and hardware behavior.