Logic Gates

A logic gate is a tiny circuit that looks at one or more inputs, each 0 or 1, and produces an output of 0 or 1 according to a simple rule:

• AND: output is 1 only if A and B are both 1. (The key is in AND the door is open: beep.)
• OR: output is 1 if A or B (or both) is 1. (Either door open: turn on the dome light.)
• NOT: one input, and the output is the opposite. (Bright, 1, in: night light off, 0, out. Dark, 0, in: night light on, 1, out.)

A truth table lists every possible input combination and the output for each.

Three more gates come up often: NAND (NOT AND: 0 only when both inputs are 1), NOR (NOT OR: 1 only when both inputs are 0) and XOR (exclusive OR: 1 when the inputs are different).

Gates are built from transistors. You’ve already seen the idea: in the Touch Switch and Night Light, a transistor turns an output on or off depending on its input. Two transistor switches in series make an AND; two in parallel make an OR.

You can try gates for real with chips from the common 74HC family, such as the 74HC08 (four AND gates in one chip), powered by a 3 × AA (4.5 V) battery pack. 74HC chips are rated for 2 to 6 V, so never use a 9 V battery. Connect any unused inputs to + or −, because a floating input can make the chip behave unpredictably.

NAND is called a universal gate: any logic circuit at all can be built from NAND gates alone (NOR is universal too). For example, a NOT is a NAND with both inputs joined.

An XOR and an AND together make a half adder, which adds two bits: XOR gives the sum bit and AND gives the carry. Chain adders together and you can add numbers of any size. That’s the beginning of how a computer’s processor does arithmetic.

0. AND needs both inputs to be 1.

XOR (exclusive OR).

Any logic circuit can be built from NAND gates alone.