OR gate

Key takeaways

OR gate belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect OR gate to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of OR gate from memory before moving on to harder problems.

Reference excerpt

The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels.

Description

Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible logical states. In addition to 1 and 0, these states may be called true and false, high and low, active and inactive, or other such pairs of symbols. Thus it performs a logical disjunction (∨) from mathematical logic. The gate can be represented with the plus sign (+) because it can be used for logical addition. Equivalently, an OR gate finds the maximum between two binary digits, just as the AND gate finds the minimum. Together with the AND gate and the NOT gate, the OR gate is one of three basic logic gates from which any Boolean circuit may be constructed. All other logic gates may be made from these three gates; any function in binary mathematics may be implemented with them. It is sometimes called the inclusive OR gate to distinguish it from XOR, the exclusive OR gate. The behavior of OR is the same as XOR except in the case of a 1 for both inputs. In situations where this never arises (for example, in a full-adder) the two types of gates are interchangeable. This substitution is convenient when a circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip.

Symbols There are two logic gate symbols currently representing the OR gate: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol. The DIN symbol is deprecated. The "≥1" on the IEC symbol indicates that the output is activated by at least one active input.

As of Unicode 16.0.0, the OR gate is also encoded in the Symbols for Legacy Computing Supplement block as U+1CC15 𜰕 LOGIC GATE OR.

Hardware description and pinout

OR gates are basic logic gates, and are available in TTL and CMOS ICs logic families. The standard 4000 series CMOS IC is the 4071, which includes four independent two-input OR gates. The TTL device is the 7432. There are many offshoots of the original 7432 OR gate, all having the same pinout but different internal architecture, allowing them to operate in different voltage ranges and/or at higher speeds. In addition to the standard 2-input OR gate, 3- and 4-input OR gates are also available. In the CMOS series, these are:

4075: triple 3-input OR gate 4072: dual 4-input OR gate Variations include:

74LS32: quad 2-input OR gate (low power Schottky version) 74HC32: quad 2-input OR gate (high speed CMOS version) - has lower current consumption/wider voltage range 74AC32: quad 2-input OR gate (advanced CMOS version) - similar to 74HC32, but with significantly faster switching speeds and stronger drive 74LVC32: low voltage CMOS version of the same.

Implementations

Analytical representation

f ( a , b ) = a + b − a ∗ b {\displaystyle f(a,b)=a+b-a*b} is the analytical representation of OR gate:

f ( 0 , 0 ) = 0 + 0 − 0 ∗ 0 = 0 {\displaystyle f(0,0)=0+0-0*0=0}

f ( 0 , 1 ) = 0 + 1 − 0 ∗ 1 = 1 {\displaystyle f(0,1)=0+1-0*1=1}

f ( 1 , 0 ) = 1 + 0 − 1 ∗ 0 = 1 {\displaystyle f(1,0)=1+0-1*0=1}

f ( 1 , 1 ) = 1 + 1 − 1 ∗ 1 = 1 {\displaystyle f(1,1)=1+1-1*1=1}

OR gates with many inputs OR gates with multiple inputs are designated with the same symbol, with more lines leading in. While direct implementations with more than three inputs are possible in logic families like CMOS, these are inefficient. More efficient implementations use a cascade of NOR and NAND gates, as shown in the picture below.

Alternatives

If no specific OR gates are available, one can be made from NAND or NOR gates in the configuration shown in the image below. Any logic gate can be made from a combination of NAND or NOR gates.

Wired-OR

With active low open collector logic outputs, as used for control signals in many circuits, an OR function can be produced by wiring together several outputs. This arrangement is called a wired OR. This implementation of an OR function typically is also found in integrated circuits of N or P-type only transistor processes.

Illustrations

Worked examples

Example 1 — a first encounter with OR gate

Start with the simplest possible case. Write down what OR gate claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to OR gate before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about OR gate ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of OR gate

In research: OR gate appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses OR gate in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: OR gate is common in secondary-school and first-year university syllabi. It links to neighbouring topics Boolean algebra, Digital electronics, Logic gates, so understanding it makes those chapters shorter.
In everyday life: Look for OR gate outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study OR gate in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what OR gate means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain OR gate out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is OR gate in simple terms?

The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false".

Why does OR gate matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study OR gate?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on OR gate.