A half adder is the simplest digital circuit that performs binary addition. It takes two single-bit inputs, A and B, and produces two outputs: a Sum bit and a Carry bit. You can build one using just two logic gates, and the whole project works on a small breadboard in under an hour.
What a Half Adder Actually Does
Binary addition follows the same rules as decimal addition, just with only two digits: 0 and 1. When you add 0 + 0, you get 0. When you add 0 + 1 or 1 + 0, you get 1. The interesting case is 1 + 1, which equals 10 in binary (that’s “2” in decimal). The “0” stays in the current column as the Sum, and the “1” moves to the next column as the Carry.
A half adder handles exactly this logic. Here’s the complete truth table:
- A = 0, B = 0: Sum = 0, Carry = 0
- A = 0, B = 1: Sum = 1, Carry = 0
- A = 1, B = 0: Sum = 1, Carry = 0
- A = 1, B = 1: Sum = 0, Carry = 1
Look at the Sum column: it outputs 1 only when A and B are different. That’s the definition of an XOR (exclusive OR) gate. Now look at the Carry column: it outputs 1 only when both A and B are 1. That’s a standard AND gate. So the Boolean expressions are simply:
- Sum = A XOR B
- Carry = A AND B
That’s the entire circuit: one XOR gate and one AND gate, both receiving the same two inputs.
Parts You Need
To build a physical half adder on a breadboard, you need:
- 1x 74LS86 (or 7486): A chip containing four XOR gates. You’ll use one gate.
- 1x 74LS08 (or 7408): A chip containing four AND gates. You’ll use one gate.
- 2x LEDs (red works well): One to display the Sum output, one for the Carry.
- 4x 1kΩ resistors: Two protect the LEDs from current spikes, and two act as pull-down resistors for the inputs.
- 1x breadboard
- 1x breadboard power supply or 5V source: Both chips run on 5V. For TTL (74LS series), logic “high” is 2.0V to 5.5V, and logic “low” is 0V to 0.8V.
- Jumper wires
- 2x switches or pushbuttons (optional): These let you toggle inputs A and B. Without switches, you can manually connect input wires to the power rail (high) or ground rail (low).
Understanding the IC Pinouts
Both the 7486 and the 7408 are 14-pin chips with the same general layout. Pin 14 is VCC (connect to +5V) and pin 7 is GND (connect to ground). These power pins supply all four gates inside each chip, so you only wire power once per chip.
Each gate on the chip uses two input pins and one output pin. On both chips, the first gate uses pins 1 and 2 as inputs and pin 3 as output. That’s the gate you’ll use. The remaining three gates on each chip sit idle, which is perfectly fine.
Wiring the Circuit Step by Step
Start by placing both ICs on the breadboard so they straddle the center divider. This ensures each pin gets its own electrical row. Connect pin 14 of both chips to your +5V rail and pin 7 of both chips to ground.
Next, pick two rows on the breadboard to serve as your A and B input lines. Run a jumper from input A to pin 1 on the 7486 (XOR chip) and also to pin 1 on the 7408 (AND chip). Do the same for input B: connect it to pin 2 on both chips. Both gates now share the same A and B signals.
For the outputs, connect pin 3 of the 7486 (the XOR output, which is your Sum) to the longer leg of one LED. Connect the shorter leg of that LED through a 1kΩ resistor to ground. Repeat for pin 3 of the 7408 (the AND output, which is your Carry) with the second LED and resistor.
If you’re using toggle switches for inputs, wire each switch so it connects the input line to +5V when closed. Add a 1kΩ pull-down resistor between each input line and ground so the input defaults to logic low when the switch is open. Without pull-down resistors, the inputs float at unpredictable voltages and the LEDs will behave erratically.
Testing All Four Input Combinations
Once wired, power the circuit and step through all four combinations from the truth table. With both inputs low (switches off), neither LED should light up. Toggle A high while keeping B low: the Sum LED should light, and the Carry LED should stay dark. Swap, so only B is high: same result. Finally, set both A and B high: the Sum LED should go dark and the Carry LED should light up, representing the binary result “10.”
If an LED stays dark when it shouldn’t, check that it’s oriented correctly (long leg toward the chip output, short leg toward ground through the resistor). You can also use a multimeter set to DC voltage mode to probe pin 3 on each chip. A reading near 5V means logic high, and a reading near 0V means logic low. If a gate output doesn’t match the truth table, double-check that VCC and GND are connected properly to that chip.
For the continuity test approach, power off the circuit first, then set your multimeter to continuity mode (usually marked with a sound wave symbol). Touch the probes together to confirm a beep, then use it to verify your wiring paths are actually connected where you intended.
Building With NAND Gates Only
If you only have a 7400 (quad NAND gate) chip, you can still build a half adder. Any logic function can be constructed from NAND gates alone. An XOR gate requires four NAND gates, and an AND gate requires two NAND gates (a NAND followed by a NAND used as an inverter). So a single 7400 chip with its four NAND gates isn’t quite enough for the full half adder. You’d need two 7400 chips, using six of the eight available gates. This approach is less tidy but demonstrates a core principle of digital logic: NAND is a universal gate.
Where a Half Adder Falls Short
The word “half” isn’t arbitrary. A half adder only handles two inputs: A and B. It has no way to accept a carry-in from a previous addition. This means it works for adding the least significant bit of two binary numbers (where there’s no prior carry to worry about), but it can’t handle any column beyond the first.
A full adder solves this by adding a third input for carry-in, producing the same Sum and Carry outputs but accounting for all three bits. To add two 8-bit numbers, you’d cascade eight full adders together, with each carry output feeding into the next stage’s carry input. The first stage can technically be a half adder since its carry-in is always zero, but in practice, designers often use full adders throughout and simply tie the first carry-in to ground.
A full adder can always replace a half adder by setting carry-in to zero, but the reverse isn’t true. So while a half adder is a great learning project, real multi-bit addition circuits rely on full adders for carry propagation.