A logic circuit is a physical implementation of Boolean logic using electronic components called logic gates. Every logic gate takes one or more binary inputs (0 or 1) and produces a single binary output. Circuits combine gates to perform more complex operations — the same logic that powers computer processors, memory, and decision-making.
In OCR J277, you need to: recognise the symbols for AND, OR, NOT (and NAND, NOR, XOR); read circuits to produce truth tables; and derive Boolean expressions from diagrams.
Gate Symbols (OCR J277)
──┐
├─[ AND ]──
──┘
AND Gate
D-shaped body with flat left side. Two or more inputs on left, one output on right.
Output = A AND B · Output is 1 only when ALL inputs are 1
──┐
├─[ OR ]───
──┘
OR Gate
Curved body (shield shape). Curved back on left side to distinguish from AND.
Output = A OR B · Output is 1 when AT LEAST ONE input is 1
──[ NOT ]──○──
NOT Gate (Inverter)
Triangle pointing right with a small circle (bubble) on the output.
Output = NOT A · Output is the inverse of the input
──┐
├─[AND]──○──
──┘
NAND Gate
AND gate with a bubble (circle) on the output. NAND = NOT AND.
Output = NOT (A AND B) · Output is 0 only when ALL inputs are 1
──┐
├─[ OR ]──○──
──┘
NOR Gate
OR gate with a bubble on the output. NOR = NOT OR.
Output = NOT (A OR B) · Output is 1 only when ALL inputs are 0
──┐
├─[ XOR ]──
──┘
XOR Gate (Exclusive OR)
OR gate with an extra curved line on the left input side.
Output = A XOR B · Output is 1 when inputs are DIFFERENT
Truth Tables for All Gates
A
B
AND
OR
NAND
NOR
XOR
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
NOT has only one input: NOT 0 = 1, NOT 1 = 0.
Reading Logic Circuits — Step by Step
To evaluate a logic circuit with given input values:
Step 1: Identify inputs A, B, C... on the left of the diagram.
Step 2: Work left to right through each gate, substituting values.
Step 3: Write the output of each gate on the wire leaving it.
Step 4: The rightmost wire is the final output.
Worked Example — Deriving a Truth Table
Circuit: A and B enter an AND gate. The output of the AND gate and C enter an OR gate. Final output = X.
Boolean expression: X = (A AND B) OR C
A
B
C
A AND B
X = (A AND B) OR C
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
Worked Example — A NOT Gate in a Circuit
Circuit: A enters a NOT gate → output is NOT A. Then NOT A and B enter an AND gate. Output = X.
Boolean expression: X = (NOT A) AND B
A
B
NOT A
X = (NOT A) AND B
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
Exam tip: In OCR J277 exams, logic circuit questions typically ask you to: (1) complete a truth table from a given circuit — always work left to right and add intermediate columns; (2) write a Boolean expression from a diagram; (3) identify which type of gate is shown. NAND and NOR are inverses of AND and OR — just flip all the outputs. XOR gives 1 only when inputs DIFFER (useful for detecting inequality).
⚠️ Common Mistakes
Confusing NAND and NOR symbols — NAND has AND body + bubble; NOR has OR body + bubble
Forgetting to include intermediate columns in truth tables (AND gate output before OR gate)
Confusing XOR with OR — XOR is 0 when BOTH inputs are 1; OR is 1
Reading circuits right to left instead of left to right
Writing the Boolean expression in the wrong order — follow wire flow from input to output
✅ Notes completed!
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Worksheet — 2.4.1b Logic Circuits
8 questions · 22 marks
Q1State the Boolean expression for: a NAND gate with inputs A and B.[1]
✅ Mark scheme
NOT (A AND B) [1]. A NAND gate is an AND gate followed by a NOT gate — it inverts the AND output. It is 0 only when A=1 AND B=1.
Q2Complete the truth table for X = (NOT A) OR B. Include a column for NOT A.[4]
✅ Mark scheme
A=0,B=0: NOT A=1, X=1 [1]. A=0,B=1: NOT A=1, X=1 [1]. A=1,B=0: NOT A=0, X=0 [1]. A=1,B=1: NOT A=0, X=1 [1].
Q3Complete the truth table for a NOR gate (A=0,B=0: ? ; A=0,B=1: ? ; A=1,B=0: ? ; A=1,B=1: ?)[4]
✅ Mark scheme
A=0,B=0: 1 [1]. A=0,B=1: 0 [1]. A=1,B=0: 0 [1]. A=1,B=1: 0 [1]. NOR is NOT(OR) — inverts the OR truth table. Only 1 when ALL inputs are 0.
Q4A circuit has A and B entering an AND gate, then the AND output and C entering an OR gate. Write the Boolean expression and evaluate when A=1, B=1, C=0.[3]
✅ Mark scheme
Boolean expression: X = (A AND B) OR C [1]. A AND B = 1 AND 1 = 1 [1]. X = 1 OR 0 = 1 [1]. Answer: X = 1.
Q5Explain the difference between the output of an AND gate and a NAND gate for the same inputs.[2]
✅ Mark scheme
NAND is the inverse (NOT) of AND [1]. For every combination of inputs, the NAND output is the opposite of the AND output — if AND gives 1, NAND gives 0, and vice versa [1].
Q6What makes XOR different from OR? Give an example using A=1 and B=1.[2]
✅ Mark scheme
XOR outputs 1 only when inputs are DIFFERENT [1]. When A=1 and B=1 (inputs are the same), OR gives 1 but XOR gives 0 [1]. XOR = "exclusive or" — one or the other, but not both.
Q7Describe the symbol used for a NOT gate, and explain how it differs from AND and OR gates.[2]
✅ Mark scheme
A triangle pointing right with a small circle (bubble) on the output [1]. Unlike AND and OR (which take TWO inputs), NOT takes only ONE input and inverts it [1].
Q8A circuit has three inputs: A, B, C. A and B go into an OR gate. The OR output and C go into a NAND gate. Complete the truth table for all 8 input combinations.[4]
Q1What is the output of a NAND gate when A=1 and B=1?
Q2A NOR gate has inputs A=0, B=0. What is the output?
Q3A=1, B=0. What is A XOR B?
Q4Which symbol distinguishes a NOT gate from other gates?
Q5A=1, B=1, C=0. Circuit: A,B → AND → then result,C → OR. Final output?
Section B — Short Answer [16 marks]
Q6Explain what a NAND gate does and how its truth table relates to an AND gate.
Mark schemeNAND = NOT AND. It takes the output of an AND gate and inverts it [1]. Every output that AND produces is flipped: where AND gives 1, NAND gives 0, and vice versa [1].
Q7Complete the XOR truth table for all 4 combinations of A and B.
Mark scheme0,0→0 [1]; 0,1→1 [1]; 1,0→1 [1]; 1,1→0 [1]. XOR is 1 when inputs are different, 0 when they are the same.
Q8A logic circuit has inputs A and B. A goes into a NOT gate (output = NOT A). NOT A and B enter an AND gate. Write the Boolean expression and evaluate for A=0, B=1.
Mark schemeExpression: (NOT A) AND B [1]. NOT A = NOT 0 = 1 [1]. 1 AND B = 1 AND 1 = 1 [1]. Final output: 1.
Q9Explain how to determine the output of a logic circuit step by step.
Mark schemeIdentify inputs on the left [1]. Work from left to right through each gate [1]. Write the output of each gate on its output wire, substituting values [1]. The final wire on the right is the circuit's output [1].
Q10Why might a logic designer use a NAND gate instead of an AND gate followed separately by a NOT gate?
Mark schemeA NAND gate combines the AND and NOT operations into a single gate component [1]. This reduces the number of physical components needed (fewer gates), saving space and cost on a circuit board [1]. NAND gates are also functionally complete — any logic circuit can be built from NAND gates alone [1].