Build a Full Adder

CSC-116 · Semester I · Digital Logic

intermediate25 minAvailable

Live simulation10 components · 12 wires

OFF

Cin

OFF

XOR

AND

XOR

AND

Sum0

Carry0

Click a switch to toggle it · drag output → input to wire · drag to move · Delete removes the selection · Ctrl+Z undoes.

Truth table

live from the current circuit

A	B	Cin	Sum	Carry
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Lab brief

Objective

Extend the half adder into a full adder that adds two bits together with a carry-in, producing a two-bit result.

Theory & concepts

A half adder cannot chain additions because it has no carry input. The full adder accepts a carry-in Cin from a previous stage. Its outputs are Sum = A XOR B XOR Cin and Carry = (A AND B) OR (Cin AND (A XOR B)).

Rendering diagram…

Full adder: sum and carry-out logic

Sum   = A XOR B XOR Cin
Carry = (A AND B) OR (Cin AND (A XOR B))

A B Cin | Sum Carry
0 0  0  |  0   0
0 1  0  |  1   0
1 1  1  |  1   1

Prerequisites

Lesson: Logic gates and truth tables
Lab: Build a Half Adder

Instructions

1Add three switches: A, B and Cin.
2Add two XOR gates, two AND gates and one OR gate.
3Wire A and B into the first XOR and the first AND.
4Wire the first XOR output and Cin into the second XOR and the second AND.
5Wire the first AND and the second AND into the OR gate.
6Send the second XOR to the Sum LED and the OR to the Carry LED.
7Test all eight input combinations against the truth table.

Tasks

Chain it up
Build the full adder and verify 1 + 1 + 1 = 11.
Compare with half adder
Explain what the extra XOR, AND and OR add over the half adder.
Multi-bit preview
Describe how full adders cascade to add multi-bit numbers.

Self-check

The circuit matches the full-adder truth table for all eight input combinations.
The student explains the role of the carry-out chain.
The student can connect the design to multi-bit addition.

Environment

gate palettewire connectionslive simulationtruth table check