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Logic gates are the fundamental building blocks of all digital circuits. Every processor, memory chip, and digital device is constructed from combinations of these simple components. For the OCR H446 specification, you must understand AND, OR, NOT, NAND, NOR, and XOR gates — their symbols, behaviour, and truth tables.
A logic gate is an electronic component that takes one or more binary inputs (0 or 1) and produces a single binary output based on a specific logical rule. Gates are the physical implementation of Boolean algebra operations.
| Concept | Detail |
|---|---|
| Inputs | Binary values: 0 (LOW / FALSE) or 1 (HIGH / TRUE) |
| Output | A single binary value determined by the gate's rule |
| Voltage levels | Typically 0V for logic 0, 3.3V or 5V for logic 1 |
The NOT gate has a single input and produces the complement (opposite) of that input.
Boolean expression: Q = NOT A (also written as A with a bar above, or A')
Truth table:
| A | Q |
|---|---|
| 0 | 1 |
| 1 | 0 |
The NOT gate is the simplest gate. It is often drawn as a triangle with a small circle (bubble) at the output. In the rectangular (IEC) notation, it is labelled with a "1" and has the inversion bubble.
Key Term: The small circle at the output of a gate symbol indicates inversion (negation). This bubble appears on NOT, NAND, and NOR gates.
The AND gate outputs 1 only when all inputs are 1.
Boolean expression: Q = A AND B (also written A . B or A * B)
Truth table:
| A | B | Q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Think of AND as a series circuit — both switches must be closed for current to flow.
Distinctive shape symbol: A flat left edge with a curved right edge. Rectangular (IEC) symbol: A rectangle labelled "&".
The OR gate outputs 1 when at least one input is 1.
Boolean expression: Q = A OR B (also written A + B)
Truth table:
| A | B | Q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Think of OR as a parallel circuit — if either switch is closed, current flows.
Distinctive shape symbol: A curved left edge with a pointed right edge. Rectangular (IEC) symbol: A rectangle labelled ">=1".
NAND stands for NOT AND. It is an AND gate followed by a NOT gate. The output is 1 unless all inputs are 1.
Boolean expression: Q = NOT(A AND B)
Truth table:
| A | B | Q |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NAND is the inverse of AND — compare the two truth tables and you will see every output is flipped.
Distinctive shape symbol: AND gate shape with an inversion bubble at the output. Rectangular (IEC) symbol: A rectangle labelled "&" with an inversion bubble.
Exam Tip: NAND gates are called universal gates because any other logic gate can be built using only NAND gates. This is a commonly tested fact in OCR H446 exams.
NOR stands for NOT OR. It is an OR gate followed by a NOT gate. The output is 1 only when all inputs are 0.
Boolean expression: Q = NOT(A OR B)
Truth table:
| A | B | Q |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
NOR is the inverse of OR.
Distinctive shape symbol: OR gate shape with an inversion bubble at the output. Rectangular (IEC) symbol: A rectangle labelled ">=1" with an inversion bubble.
NOR is also a universal gate — any logic function can be constructed from NOR gates alone.
The XOR gate outputs 1 when the inputs are different.
Boolean expression: Q = A XOR B (also written A (+) B)
Truth table:
| A | B | Q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
XOR differs from OR in one key row: when both inputs are 1, OR outputs 1 but XOR outputs 0.
Distinctive shape symbol: Like OR but with an extra curved line on the left. Rectangular (IEC) symbol: A rectangle labelled "=1".
Key Term: XOR is sometimes called the "difference detector" — it outputs 1 when the inputs differ and 0 when they are the same.
| Gate | Expression | Output = 1 when... | Universal? |
|---|---|---|---|
| NOT | NOT A | Input is 0 | No |
| AND | A AND B | All inputs are 1 | No |
| OR | A OR B | At least one input is 1 | No |
| NAND | NOT(A AND B) | Not all inputs are 1 | Yes |
| NOR | NOT(A OR B) | All inputs are 0 | Yes |
| XOR | A XOR B | Inputs are different | No |
AND, OR, NAND, NOR, and XOR gates can all have more than two inputs.
3-input AND gate truth table:
| A | B | C | Q = A AND B AND C |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
For a 3-input AND gate, the output is 1 only when A = B = C = 1.
For a 3-input OR gate, the output is 1 when any input is 1.
Question: Draw the truth table for the expression Q = (A AND B) OR (NOT C).
Step 1: List all input combinations for A, B, and C (2^3 = 8 rows). Step 2: Calculate intermediate values: A AND B, and NOT C. Step 3: Combine using OR.
| A | B | C | A AND B | NOT C | Q = (A AND B) OR (NOT C) |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
Exam Tip: Always show intermediate columns in truth tables. This earns method marks even if the final column has errors.