Cambridge IGCSE 0478 · Topic 3 · 3.1b

NAND, NOR &
XOR Gates

Combined Gates · Truth Tables · Logic Circuits

CSZoneCambridge IGCSE Computer Science 0478

NAND & NOR Gates

AND/OR with NOT Appended

NAND = NOT(AND)

A	B	Out
0	0	1
0	1	1
1	0	1
1	1	0

Output = 0 only when BOTH = 1

NOR = NOT(OR)

A	B	Out
0	0	1
0	1	0
1	0	0
1	1	0

Output = 1 only when BOTH = 0

XOR Gate

Exclusive OR

XOR (A ⊕ B)

A	B	Out
0	0	0
0	1	1
1	0	1
1	1	0

XOR: output is 1 when inputs are different. Output is 0 when inputs are the same.

XOR is used in binary addition circuits and encryption (bitwise XOR)

Logic Circuits & Expressions

Combining Gates

Expression: X = (A AND B) OR (NOT C)

Step 1: calculate A AND B
Step 2: calculate NOT C
Step 3: OR the results → X

For A=1, B=0, C=1:
A AND B = 0; NOT C = 0; X = 0 OR 0 = 0

Always evaluate sub-expressions inside brackets first (inner gates first)

NAND is a universal gate — all other gates can be built from NAND gates alone

Exam Practice

Have a go at this question

Cambridge IGCSE 0478 style

Complete the truth table for the expression: X = (A NAND B) AND C, for all combinations of A, B, and C.

4 marks

A NAND B: 00→1, 01→1, 10→1, 11→0. Then AND with C: 0,0,0,0 (for C=0 rows) and 1,1,1,0 (for C=1 rows). [1 per correct pair of rows, max 4]

Key Takeaways

What to Remember

NAND = NOT(AND): output 0 only when both inputs are 1

NOR = NOT(OR): output 1 only when both inputs are 0

XOR: output 1 when inputs are different (0,1 or 1,0)

Logic circuits: trace from inputs through each gate to get the final output