Logic Gates & Truth Tables

A logic gate is a tiny circuit that takes one or more binary inputs and produces a binary output according to a fixed rule. Every digital system, including your Arduino's processor, is built from millions of these gates.

The behavior of a gate is described by a truth table: a list of every possible input combination and the output for each one. A gate with n inputs has 2ⁿ rows in its truth table.

NOT (inverter)     AND              OR
A | Y              A B | Y          A B | Y
0 | 1              0 0 | 0          0 0 | 0
1 | 0              0 1 | 0          0 1 | 1
                   1 0 | 0          1 0 | 1
                   1 1 | 1          1 1 | 1

NAND               NOR              XOR
A B | Y            A B | Y          A B | Y
0 0 | 1            0 0 | 1          0 0 | 0
0 1 | 1            0 1 | 0          0 1 | 1
1 0 | 1            1 0 | 0          1 0 | 1
1 1 | 0            1 1 | 0          1 1 | 0

• NOT: output is the opposite of the input
• AND: output is 1 only when all inputs are 1
• OR: output is 1 when at least one input is 1
• NAND: AND followed by NOT (0 only when all inputs are 1)
• NOR: OR followed by NOT (1 only when all inputs are 0)
• XOR (exclusive OR): output is 1 when the inputs are different

Logic gates come packaged in 14-pin chips. The 74HC series works at 5V, so it pairs well with an Arduino Uno. Each chip holds several identical gates that share one power connection.

• 74HC08: four 2-input AND gates
• 74HC32: four 2-input OR gates
• 74HC04: six NOT gates (hex inverter)
• 74HC00: four 2-input NAND gates
• 74HC86: four 2-input XOR gates

74HC08 / 74HC00 / 74HC32 / 74HC86 pinout (top view, notch on the left)

  1A  [1]  ● [14] VCC
  1B  [2]    [13] 4B
  1Y  [3]    [12] 4A
  2A  [4]    [11] 4Y
  2B  [5]    [10] 3B
  2Y  [6]    [9]  3A
  GND [7]    [8]  3Y

Instead of flipping switches by hand, let the Arduino drive the gate's inputs, read its output, and print the whole truth table.

• Chip pin 14 → 5V, pin 7 → GND
• 100nF capacitor directly between pins 14 and 7
• Arduino pin 2 → chip pin 1 (input A), Arduino pin 3 → chip pin 2 (input B)
• Chip pin 3 (output Y) → Arduino pin 4, and also → 470Ω → LED → GND
• Tie the inputs of the three unused gates (pins 4, 5, 9, 10, 12, 13) to GND

const int inA = 2, inB = 3, gateOut = 4;

void setup() {
  pinMode(inA, OUTPUT);
  pinMode(inB, OUTPUT);
  pinMode(gateOut, INPUT);
  Serial.begin(9600);

  Serial.println("A B | Y");
  for (int a = 0; a <= 1; a++) {
    for (int b = 0; b <= 1; b++) {
      digitalWrite(inA, a);
      digitalWrite(inB, b);
      delay(5);  // let the output settle
      Serial.print(a); Serial.print(" "); Serial.print(b);
      Serial.print(" | ");
      Serial.println(digitalRead(gateOut));
    }
  }
}

void loop() {}

• Swap in a 74HC00, 74HC32, and 74HC86 and confirm each truth table matches the section above.
• Chain two gates of the 74HC08 to build a 3-input AND, and extend the tester to 3 inputs (8 rows).
• Add a check that compares each reading with the expected value and prints PASS or FAIL, turning the sketch into a chip tester.