PAPER 1 • BOOLEAN ALGEBRA

Half and Full Adders

A half adder adds two one-bit inputs, A and B, and produces a sum output Digit plus a carry output Cout.
A full adder extends this by adding a third input, Cin, so it can include a carry from the previous stage of a larger binary addition while still outputting Digit and Cout.
Work through the two activities in order: build each circuit in the simulator, complete the truth table, then explain what the outputs show.

Visual channel

Dual coding

Verbal channel

A half adder has two inputs and is useful for adding a single pair of bits when there is no incoming carry.
The sum output Digit behaves like an XOR gate because it is 1 only when exactly one input is 1.
The carry output Cout behaves like an AND gate because it is 1 only when both inputs are 1.
A full adder accepts A, B and Cin, then outputs Digit and Cout so addition can continue across multiple bits.

Activity 1

Build a Half Adder

Use the simulator to build a circuit with two inputs labelled A and B.
Create outputs labelled Digit and Cout. Your finished circuit should behave as a half adder.
Hint: one output is the sum bit and the other is the carry bit created when both inputs are 1.

Logic gates only

Explain what the circuit does. You should refer to A, B, Digit and Cout in your answer.

Activity 2

Use the simulator to build a full adder with inputs A, B and Cin.
Create outputs labelled Digit and Cout. This circuit must include the carry from a previous calculation.
Hint: a full adder can be thought of as two half adders joined together with an OR gate for the carry outputs.

Logic gates only

Describe the difference between a half adder circuit and a full adder circuit.