2-Input OR Gate
Two switches drive an inclusive OR gate and one output light. The output is LOW only for 00 and HIGH for the other three binary input combinations.
What You'll Learn
- Read and write the 2-input OR truth table from memory.
- Recognize that OR is the dual of AND — it returns 0 only when every input is 0.
- Translate "or" / "either" / "any of" English statements into Boolean OR.
- Identify OR gates inside larger circuits like alarms, interrupts, and reset trees.
- Understand why OR is commutative and associative, and why those properties matter.
How It Works
A Boolean OR implements inclusive disjunction: Output is high when A is high, B is high, or both are high. Only A = B = 0 produces a low output. The function is Output = A + B, where + denotes logical OR rather than arithmetic addition.
The production circuit connects two input switches to one 2-input OR gate and connects that gate to one output light. Three of the four input combinations drive the light high. By comparison, a 2-input AND is high on only the 11 row; this is a complementary row-count pattern, not a claim that OR is the logical negation of AND.
OR is commutative (A + B = B + A) and associative ((A + B) + C = A + (B + C)). Those identities preserve the stable logic function when inputs are reordered or grouped. In physical hardware, different groupings can still change gate depth, delay, area, and transient behavior.
Truth Table
A 2-input OR has 2² = 4 possible combinations. Only the all-zeros row produces 0; every other row produces 1.
| Inputs | Output | ||
|---|---|---|---|
| A | B | Output | |
| 0 | 0 | 0 | Both off — output low |
| 0 | 1 | 1 | One input high — output high |
| 1 | 0 | 1 | |
| 1 | 1 | 1 | Both high — output still high |
Boolean Expression
Standard form. The + denotes logical OR, not arithmetic addition.
Formal logic notation using the disjunction symbol.
De Morgan equivalent — OR equals NAND of the inverted inputs.
Try It Step-by-Step
Set the listed controls in the embedded circuit, then compare the observed modeled state with the expected result.
- 1A=0B=0Expected:
Output = 0What you'll see:Both switches off — the output is dark. This is the only combination that produces 0. - 2A=1B=0Expected:
Output = 1What you'll see:One input high — output goes high. OR doesn't care which input lifts it, just that at least one does. - 3A=0B=1Expected:
Output = 1What you'll see:Symmetry: flipping which input is high gives the same result. OR is commutative. - 4A=1B=1Expected:
Output = 1What you'll see:Both inputs high — output stays high. Unlike XOR, OR doesn't flip back to 0 when both inputs match.
Components Used
Applications and Design Context
Alarm-request aggregation. Conditioned window, motion, and glass-break signals can feed an OR so any active request asserts an aggregate alarm.
Interrupt aggregation. Peripheral request lines can be ORed into one processor-facing interrupt, while separate status or vector logic identifies the source.
Active-high reset requests. Power-on, watchdog, manual, and debug reset requests can be combined before reset distribution, subject to polarity and synchronization requirements.
Status summaries. Independent fault bits can drive a master warning without discarding the detailed per-fault indicators.
Array error summaries. Local memory-bank error flags can be ORed into one aggregate error signal.
Frequently Asked Questions
Is OR the same as inclusive-or in English?
Yes. Boolean OR is the inclusive sense: "A or B or both." The exclusive sense ("A or B but not both") is XOR — a different gate.
Why does + mean OR instead of addition?
It's a notational convention from George Boole's algebra. In Boolean expressions, + is OR and · is AND — different operators that share symbols with arithmetic for historical reasons.
Can I build an OR gate using only NAND gates?
Yes. NAND is universal — any logic function, including OR, can be built from NANDs alone. Specifically: A OR B = NAND(NOT A, NOT B), and NOT A = NAND(A, A).
What's the OR of more than two inputs?
It is high when at least one input is high. A wider OR can be realized with a wide-fan-in cell or a tree of smaller gates. Associativity preserves the steady-state Boolean result, while grouping still affects physical depth and timing.
What's the difference between OR and XOR?
OR returns 1 when at least one input is 1 (including when both are 1). XOR returns 1 only when an odd number of inputs are 1 — it's 0 when both inputs are 1. They differ on exactly the row where both inputs are high.