Adder Circuits and Flip-Flops

This lesson covers two essential building blocks of digital systems: adder circuits (used for binary arithmetic) and flip-flops (used for memory and sequential logic). At A-Level you must be able to draw, analyse, and explain both.

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Half Adder

A half adder adds two single-bit binary numbers and produces a sum (S) and a carry (C).

Truth Table

A	B	Sum (S)	Carry (C)
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Boolean Expressions

• S = A ⊕ B (XOR)
• C = A . B (AND)

Circuit

A ──┬──→ [XOR] ──→ S (Sum)
    │      ↑
B ──┼──────┘
    │
    └──→ [AND] ──→ C (Carry)
         ↑
B ───────┘

The half adder is called "half" because it has no carry input — it cannot handle a carry from a previous stage.

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Full Adder