Write the Boolean expression for (i) OR gate, (ii) AND gate, and (iii) NAND Gate.

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Accepted Answer

(i) OR gate: the output Y is 1 (high) whenever any one, or more than one, of the inputs is 1 -- for two inputs A and B, this is written $Y=A+B$ , where '+' denotes the logical OR operation (not ordinary addition; note $1+1=1$ in Boolean algebra). (ii) AND gate: the output Y is 1 (high) only when ALL inputs are simultaneously 1 -- for two inputs, $Y=A\cdot B$ , where ' $\cdot$ ' denotes the logical AND operation, directly analogous to ordinary multiplication of 0s and 1s. (iii) NAND gate: formed by an AND gate followed by a NOT gate (inversion), so its output is the exact complement of the AND gate's output -- $Y=\overline{A\cdot B}$ , where the overline over the whole product denotes that the ENTIRE AND result is negated (this is different from negating A and B individually before ANDing them, which would give a …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set ANNUAL1 markMCQ
$Q. The gate which produces high output, when its both inputs are high is -$
(a) X-OR gate
(b) AND gate
(c) NAND gate
(d) NOR gate
›Reveal solutionSolution

An AND gate's truth table gives a high (1) output only when every input is high.

For a two-input logic gate with inputs A, B: the AND gate follows $Y = A\cdot B$ , so $Y=1$ only when $A=1$ and $B=1$ (both inputs high); for any other input combination $Y=0$ . The OR-family and NAND/NOR gates behave differently — a NAND gate is high for every combination except both-high, and a NO …

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CBSE 2021Set A1 markMCQ
$Q. Which of the following is correct for fundamental gate? (A) AND, OR, NOT (B) AND,$
(OR)
$(C) NAND, NOR (D) OR, NOT$
›Reveal solutionSolution
The three fundamental logic gates are AND, OR and NOT.

Logic gates are the building blocks of digital circuits. The three fundamental (basic) gates are:

OR — output 1 if any input is 1 (logical addition, A+B),

AND — output 1 only if all inputs are 1 (logical multiplication, A·B),

NOT — inverts the input (Ā). …
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CBSE 2019Set ANNUAL1 mark
$Q. Mention one practical application of logic gates.$
›Reveal solutionSolution

Logic gates implement binary decision-making, so they form the core of every digital device, from calculators to computers to automated control systems.

Application

Logic gates (AND, OR, NOT, NAND, NOR, XOR) combine binary (0/1, HIGH/LOW) inputs according to Boolean rules. A practical example: in a digital calculator or computer, arithmetic and logical operations are built up entirely from networks of logic gates; another example is an automatic control circuit (e.g. a security/alarm system) that switches on an output only when a specific combination of input conditions ("sensor triggered" AND "system armed") is satisfied.

§ Honest curriculum note

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CBSE 2019Set ANNUAL1 mark
$Q. Name the logic gate which generates high output when at least one input is high.$
›Reveal solutionSolution

The logic gate that gives a high output if any one (or more) input is high is the OR gate.

…

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Q.Write the Boolean expression for

Concept understanding — Logic Gates — NOT, OR and AND Gates

Q.Write the Boolean expression for

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