XOR gate explained: build a half adder with a 74HC86 and a 74HC08

Can two chips and two LEDs add? Yes, if you only need to add two single bits. In this tutorial you will learn what an XOR gate does, see why it is exactly what binary addition needs, and wire a half adder in Mokxi using a 74HC86 and a 74HC08. By the end you will have a circuit that counts 0, 1 and 2 on a pair of LEDs.

Open this circuit in Mokxi

Add two bits on paper first

Binary addition works like decimal addition, but a column can only hold a 0 or a 1. Here are all four sums of two bits:

A	B	A + B	Carry	Sum
0	0	0	0	0
0	1	1	0	1
1	0	1	0	1
1	1	10 (two)	1	0

The last row is the interesting one. One plus one is two, and in binary two is written 10: a sum bit of 0 and a carry of 1 into the next column, the same way 9 + 1 carries in decimal.

Look at the two answer columns separately.

• The sum column is 1 when the inputs are different. That is an XOR gate (exclusive OR).
• The carry column is 1 only when both inputs are 1. That is an AND gate.

So a half adder is just one XOR and one AND sharing the same two inputs.

What an XOR gate does

XOR is "one or the other, but not both". Its output is 1 when its two inputs differ.

A	B	Y (A XOR B)
0	0	0
0	1	1
1	0	1
1	1	0

Unlike NAND or NOR, an XOR has no input value that decides the answer on its own. Whatever A is, the output still depends on B. In Mokxi's model that means an XOR with one input floating gives an unknown output. I tried it: with A high and B connected to nothing, the 74HC86 output read as unknown, not 0 or 1. Always give both inputs a definite level.

A handy trick: B acts as an on/off switch for inversion. With B at 0 the gate passes A through unchanged, and with B at 1 it flips A. I ran all four combinations to check, and the outputs were 0, 1, 1, 0.

What you need

• one 74HC86 quad XOR and one 74HC08 quad AND
• a Power part (VCC) and a Ground part (GND)
• two Slide switches, for A and B
• two LEDs (say green for sum and red for carry) and two 1 kilohm resistors

Press the + button on the canvas toolbar or the A key, search for each part's name and click its tile. Wiring is drag from pin to pin, and while you drag, Mokxi shows the name of the pin under the pointer.

Wire the half adder

Both chips use the same first-gate pins as the 74HC00 family does. Pins 1 and 2 are the inputs, pin 3 is the output, pin 7 is ground and pin 14 is the supply. Confirm it against the Texas Instruments SN74HC86 datasheet if you like.

1. Wire Power to pin 14 on both chips and Ground to pin 7 on both. These are real chips, so they do nothing until powered.
2. For each slide switch, wire pin 1 to Ground and pin 3 to Power. The middle pin, 2, is the output that moves when you click it.
3. Wire switch A's middle pin to pin 1 of the 74HC86 and pin 1 of the 74HC08.
4. Wire switch B's middle pin to pin 2 of both chips.
5. Wire the 74HC86's pin 3 through a resistor to the green LED's anode (A), and the LED's cathode (C) to Ground. This is the sum.
6. Wire the 74HC08's pin 3 through the other resistor to the red LED, with its cathode to Ground. This is the carry.
7. Press Run and click the switches.

Each input goes to two chips, so each switch pin has two wires. That is the whole idea of a half adder: both gates look at the same two bits.

Check it

I ran this exact circuit in Mokxi's headless simulator with both chips powered and the inputs on switches. Here is what the outputs gave:

A	B	Carry (red)	Sum (green)	Reads as
0	0	0	0	0
0	1	0	1	1
1	0	0	1	1
1	1	1	0	2

Read the LEDs as a two-digit binary number, carry on the left and sum on the right. With both switches up you get 10, which is two. Your circuit has just added 1 + 1.

Why it is called a half adder

It is "half" because it cannot take a carry in. To add longer numbers, each column also has to add the carry that arrived from the column on its right. A circuit that does that is a full adder, made from two half adders and an OR gate. Mokxi's half adder and full adder guide goes through the idea, and the Full adder project (search for it at /templates) wires the whole thing from a 74HC86, a 74HC08 and a 74HC32.

Things to try next

• Build the XOR from NANDs. A single 74HC00 can make an XOR from four NAND gates. Wire it, and compare its table to the 74HC86's.
• Make an inverter you can switch. Put a signal on A and a slide switch on B. With B at 0 the 74HC86 passes A through, and with B at 1 it flips A. Adders that can also subtract use exactly this trick.
• Add a carry input. Feed the sum into a second XOR and add a carry-in switch. That is the start of a full adder, which the next step up needs.
• Read the chip family notes. The 74HC logic family help page describes each chip's model, delay and common mistakes before you wire the next one.

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