Half adder with a literal 0/1 readout

This project builds a one-bit half adder from individual 74-series logic gates — an AND gate and an XOR gate, nothing more integrated than that — and reads the result out on two 7-segment displays that simply show "0" or "1". Flip switch A and switch B and watch the Sum and Carry digits respond. It's a small circuit, but it's the same building block that scales up into full binary adders inside a CPU.

Schematic

Segments b and c are wired straight to +5V because both digits this display ever shows — "0" and "1" — need them lit. Segments a, d, e and f are wired to an inverter, so they light only when the gate's output is 0 (forming a "0"); when the output is 1 they go dark, leaving just b and c lit (forming a "1"). Segment g is never used by either digit, so it's left unconnected.

Parts list

How it works

A half adder answers one question: what's A + B when A and B are single bits? Two things come out of that sum — the result bit itself (Sum) and whether the addition overflowed into a second bit (Carry). Sum is exactly what an XOR gate computes: it's 1 when the inputs differ and 0 when they match, which is precisely how binary addition behaves for a single bit. Carry is exactly what an AND gate computes: it's only 1 when both inputs are 1 — the one case where 1+1 produces a carry into the next column.

Both gate outputs are logic-level signals, not digits, so each one passes through an inverter that drives four segments of its own display. When a gate's output is 0, the inverter's output is 1, lighting segments a, d, e and f — combined with b and c, which are always lit, that traces out a "0". When the gate's output flips to 1, the inverter's output drops to 0, those four segments go dark, and only b and c remain lit — tracing a "1".

Try all four input combinations: 0+0 shows 0 and 0, 0+1 and 1+0 both show 1 and 0, and 1+1 shows 0 on Sum but 1 on Carry — the circuit's way of saying "1+1 = 10 in binary."

Build notes

• Any 74xx or 74HCxx family part works electrically the same way; 74HC parts are the easiest to find new and run happily from 5V.
• If you only have 7400 NAND gates on the bench, both gates here can be built from NAND alone, since NAND is a universal gate: AND is a NAND followed by a NAND wired as an inverter, and XOR can be built from four NAND gates — a classic exercise worth trying once you've got this version working.
• Confirm your displays are common cathode — on a common-anode display this circuit's logic is inverted throughout.
• Socket the ICs so you can freely swap the AND or XOR gate for a NAND, NOR or OR while experimenting, without re-soldering.
• This scales: chain a second half adder plus an OR gate on the carries and you've built a full adder, the block that ripples together into a multi-bit binary adder.