NOR Logic Calculator - Boolean NOR Gate & Truth Table
Calculate NOR logic operations for 2–4 inputs, generate full truth tables, and explore Boolean NOR gate behavior instantly.
Select input type and number of inputs, enter values (0/1 or True/False), and click Calculate NOR to see the result and optionally the full truth table.
NOR Logic Calculator - Boolean NOR Gate & Truth Table
Calculate NOR logic operations for 2–4 inputs, generate full truth tables, and explore Boolean NOR gate behavior instantly.
Enter 0 for FALSE and 1 for TRUE.
About the NOR logic calculator
The NOR gate is one of the fundamental building blocks of digital logic. NOR stands for NOT-OR: it first computes the logical OR of all its inputs, then inverts (negates) the result. For a two-input NOR gate, the output is 1 (TRUE) only when both inputs are 0 (FALSE); in all other cases — A=0,B=1; A=1,B=0; or A=1,B=1 — the OR is true, so its inversion is false.
The NOR gate is known as a universal gate, meaning that any Boolean logic function — AND, OR, NOT, NAND, XOR, and all combinations — can be built using only NOR gates. This property makes NOR central to digital circuit design, integrated-circuit manufacturing, and computer architecture. The NOR gate was historically significant because early TTL and CMOS logic families found NOR circuits particularly efficient to fabricate.
For multi-input NOR, the rule extends naturally: the output is 1 if and only if every single input is 0. A three-input NOR outputs 1 in exactly one row of its eight-row truth table (all inputs 0); a four-input NOR outputs 1 in exactly one row of its sixteen-row table. This means multi-input NOR gates become increasingly restrictive: the more inputs, the rarer the output-1 condition.
In Boolean algebra, NOR is written A↓B or A NOR B. De Morgan's theorem expresses the relationship between NOR and other gates: NOR(A,B) = NOT(A OR B) = NOT(A) AND NOT(B). This means a NOR gate with both inputs tied together behaves as a NOT (inverter) gate, which is one of the building-block identities used when constructing complex logic from NOR-only designs.
Practical applications of NOR logic appear in memory cells (NOR flash memory), set-reset (SR) latches built from cross-coupled NOR gates (forming the basis of flip-flops), combinational circuits in programmable logic devices (PLDs), and basic logic-probe exercises in electronics education. Understanding the NOR truth table is a prerequisite for digital electronics, computer engineering, and hardware description language (HDL) programming.
This calculator supports 2, 3, and 4-input NOR operations with both binary (0/1) and Boolean (True/False) input formats. Toggle the truth table to see all possible input combinations for the selected number of inputs.
NOR logic examples
Four examples demonstrating NOR gate behavior across input types and input counts.
| Inputs | NOR Result | Explanation |
|---|---|---|
| A=0, B=0 (binary, 2 inputs) | 1 (TRUE) | All inputs are 0, so OR is 0 and NOT(OR) = 1. This is the only all-zero combination, producing the only TRUE output in a 2-input NOR table. |
| A=0, B=1 (binary, 2 inputs) | 0 (FALSE) | OR(0,1) = 1, so NOR = NOT(1) = 0. Any single input being 1 makes the output 0. |
| A=0, B=0, C=0 (binary, 3 inputs) | 1 (TRUE) | Three-input NOR is 1 only when all inputs are 0. Out of 8 possible rows in the truth table, only this row gives output 1. |
| A=True, B=False (boolean, 2 inputs) | FALSE | NOR with Boolean input: OR(True, False) = True, so NOR = NOT(True) = False. Boolean and binary NOR are equivalent in meaning. |
How to use the NOR calculator
- Choose the Input Type: Binary (0 or 1) or Boolean (True/False or T/F). Both are equivalent — choose whichever is more natural for your context.
- Select the number of inputs: 2, 3, or 4. The corresponding input fields A through D appear automatically.
- Enter values for each input field, then click Calculate NOR. The result shows the NOR output as TRUE or FALSE with its binary equivalent.
- Click Show Truth Table to display all possible input combinations for the selected number of inputs and their corresponding NOR outputs.
- Click Reset to clear all inputs and start over.
NOR calculator FAQ
What is a NOR gate?
A NOR gate is a digital logic gate that outputs TRUE (1) only when all of its inputs are FALSE (0). It is the combination of a NOT gate placed after an OR gate: first the OR of all inputs is computed, then the result is inverted. NOR is a universal gate — any logic circuit can be constructed using only NOR gates, which makes it fundamentally important in digital design.
How does NOR differ from OR?
An OR gate outputs 1 when at least one input is 1, and 0 only when all inputs are 0. A NOR gate is the exact opposite: it outputs 0 when at least one input is 1, and 1 only when all inputs are 0. In other words, NOR is the complement (inversion) of OR. Adding a NOT inverter to the output of an OR gate produces a NOR gate.
Why is NOR called a universal gate?
A gate is universal if every Boolean function can be expressed using only that gate. NOR is universal because you can build a NOT gate (tie both inputs together), an OR gate (NOR followed by a NOR-inverter), and an AND gate (NOR the inverted inputs) — and since NOT, OR, and AND form a functionally complete set, NOR alone can replicate any circuit. NAND gates share this universality property.
What is a NOR SR latch?
An SR (Set-Reset) latch is a basic memory element built from two cross-coupled NOR gates. One gate's output feeds back as one input to the other gate. The S (Set) input forces the output to 1; the R (Reset) input forces it to 0; both inputs 0 holds the last state (memory); both inputs 1 is the forbidden state. SR latches are the foundation of flip-flops, registers, and all synchronous digital memory.
How many rows are in a 4-input NOR truth table?
A 4-input truth table has 2⁴ = 16 rows, one for each combination of the four binary inputs. The NOR output is 1 in exactly one of those 16 rows — the row where A=0, B=0, C=0, D=0. In all other 15 rows, at least one input is 1, making the OR true and the NOR false.
What is the difference between NOR and XNOR?
NOR outputs 1 only when all inputs are 0. XNOR (exclusive-NOR) outputs 1 when an even number of inputs are 1 — for two inputs, when both are 0 or both are 1. They differ everywhere except the all-zeros input row. For a 2-input truth table, NOR produces 1-0-0-0 while XNOR produces 1-0-0-1 (reading rows 00, 01, 10, 11 in order).