NAND gate tutorial for beginners: build every other gate from a 74HC00

A NAND gate is the most useful little chip in digital electronics, and it is also one of the easiest to understand. In this tutorial you will learn what a NAND gate does, wire a real 74HC00 chip in Mokxi, check its truth table with two switches and an LED, and then build NOT, AND, OR and XOR gates using nothing but NANDs.

Open this circuit in Mokxi

What a NAND gate does

NAND is short for "NOT AND". An AND gate gives a 1 only when both of its inputs are 1. A NAND gate gives the opposite answer, so its output is 0 only when both inputs are 1. Every other combination gives a 1.

A	B	Y (A NAND B)
0	0	1
0	1	1
1	0	1
1	1	0

A 0 on either input is enough to force the output high, whatever the other input is doing. Keep that rule in mind, because the rest of this post depends on it.

Here a 1 means "close to the supply voltage" (5 V in our circuit) and a 0 means "close to ground". The 74HC family runs from 2 V to 6 V, according to the Texas Instruments SN74HC00 datasheet, and typically answers in about 9 nanoseconds at 4.5 V.

Why does NAND get so much attention? It is "universal": any other logic gate, and so any digital circuit, can be built from NAND gates alone. That is the idea behind Mokxi's build a computer from NAND gates path, and you will see a small version of it below.

What you need

• one 74HC00 quad NAND chip (four NAND gates in one 14-pin package)
• a Power part (VCC) and a Ground part (GND)
• two Slide switches
• one LED and one 1 kilohm resistor

To place a part, press the round + button on the canvas toolbar (or the A key), type a name in the search box and click the tile. The placing parts guide shows the three ways to get a part onto the canvas. You can wire pin to pin, or drop the chip across the middle of a breadboard if you like.

Wire one NAND gate

The 74HC00 has four gates. The first one uses pins 1, 2 and 3:

Pin	Name	Job
1	1A	gate 1, input A
2	1B	gate 1, input B
3	1Y	gate 1, output
7	GND	ground
14	VCC	supply

1. Connect the Power part to pin 14 (VCC) and the Ground part to pin 7 (GND). A Mokxi logic chip has real power pins, so it does nothing at all until you wire them. An unpowered chip leaves its outputs disconnected, which is the most common reason a logic circuit looks dead.
2. Give each slide switch a high and a low. Wire its pin 1 to Ground and its pin 3 to Power. The middle pin, 2, is the one that moves between them when you click it.
3. Wire the first switch's pin 2 to chip pin 1, and the second switch's pin 2 to chip pin 2.
4. Wire chip pin 3 (the output) to the resistor, the resistor to the LED's anode (A), and the LED's cathode (C) to Ground. Use 1 kilohm: a chip output is happy with a few milliamps, and this value keeps the LED current around 3 mA.
5. Press Run and click the switches.

The LED should be lit for every switch position except the one with both switches at 5 V. I checked this on Mokxi's 74HC00 model for all four input pairs, and the output matched the truth table row for row.

One more habit to learn now: never leave a gate input floating. The datasheet says unused inputs must be tied to VCC or ground. Mokxi follows that, and an input that connects to nothing gives an unknown output unless the other input already decides the answer, as a 0 does on a NAND.

Every other gate, from NANDs

Now the clever part. All of these use only the four gates in one 74HC00. The gate-to-pin map is:

Gate	Inputs	Output
1	pins 1, 2	pin 3
2	pins 4, 5	pin 6
3	pins 9, 10	pin 8
4	pins 12, 13	pin 11

NOT from one NAND

Join both inputs of a gate together. If A is 0 both inputs are 0 and the output is 1. If A is 1 both inputs are 1 and the output is 0. That is an inverter.

Wire your input to pins 1 and 2 together, and read pin 3.

AND from two NANDs

AND is NAND followed by NOT. Put A on pin 1 and B on pin 2. Wire pin 3 to pins 4 and 5 (gate 2 acting as the inverter). Read pin 6.

OR from three NANDs

This one uses a rule you can remember as "invert both, then NAND". If either input is 1, at least one of the inverted inputs is 0, and a 0 forces the NAND high.

1. A goes to pins 1 and 2 (gate 1 inverts A, result on pin 3).
2. B goes to pins 4 and 5 (gate 2 inverts B, result on pin 6).
3. Wire pin 3 to pin 9 and pin 6 to pin 10 (gate 3 is the NAND).
4. Read pin 8.

XOR from four NANDs

XOR is 1 when the inputs differ. It needs the whole chip.

1. A goes to pin 1 and pin 4. B goes to pin 2 and pin 10.
2. Gate 1's output (pin 3) goes to pin 5 and pin 9.
3. Gate 2's output (pin 6) goes to pin 12. Gate 3's output (pin 8) goes to pin 13.
4. Read pin 11, gate 4's output.

Gate 1 compares A and B. Gates 2 and 3 each ask "is this input 1 while the other is 0?", and gate 4 combines the two answers.

I built all four of these in Mokxi's headless simulator, with the chip powered and the inputs on switches, and read the output for every input pair. NOT gave 1 then 0. AND gave 0, 0, 0, 1. OR gave 0, 1, 1, 1. XOR gave 0, 1, 1, 0. Each is exactly the gate you expect.

Things to try next

• NOR from NANDs. Take the OR circuit above and add gate 4 as an inverter on pin 8 (wire pin 8 to pins 12 and 13, read pin 11). It uses all four gates. Then compare your NOR with a chip made to be one, the 74HC02, which has four NOR gates in a single package.
• Latch. Cross-wire two gates so each output feeds the other's input, and you have a circuit that remembers a bit. Mokxi has a ready-made NAND latch project: search for it in the built-in projects at /templates.
• Count the chips. Work out how many NAND gates a full adder needs, then compare with building it from XOR, AND and OR chips.

For more on how gates fit together, read logic gates explained.

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