AC Electrics - Logic Gates — Page 268, Lesson 282

I want to walk you through three more logic gates that build directly on the AND and OR gates we just covered. These are the NAND gate, the NOR gate, and the EXCLUSIVE OR gate — each one is a variation of the basic gates, and each has a very specific behaviour you need to know. Let’s start with the NAND gate. The name itself tells you what it is: NAND stands for NOT AND. A NAND gate is simply an AND gate with its output inverted — that is, flipped to the opposite state. So where an AND gate gives you a ‘1’ output only when all inputs are ‘1’, the NAND gate does the exact opposite. The output of a NAND gate will be ‘1’ if any input is ‘0’. That’s the key rule: any input at zero gives you a one at the output. Only when all inputs are ‘1’ does the output become ‘0’. That is the exact opposite of an AND gate. If you look at the relay circuit representation in Figure 17.4, you’ll see that if either switch is closed, there will be no output. Let me explain that: in the relay circuit, the switches are normally closed — they conduct when not pressed. If you close either switch, you break the circuit, and the output drops to zero. So the output is ‘1’ only when both switches are open — that is, when neither input is active. That matches the truth table: output is ‘1’ when any input is ‘0’. Now, the NOR gate. NOR stands for NOT OR. A NOR gate is an OR gate with its output inverted. In an OR gate, any input being ‘1’ gives a ‘1’ output. In a NOR gate, any input being ‘1’ will create a ‘0’ output. So the output is ‘1’ only when all inputs are ‘0’. That’s the rule: all zeros in gives a one out; any one in gives a zero out. The symbol, truth table, and relay circuit for the NOR gate are all shown in Figure 17.5. Finally, the EXCLUSIVE OR gate, often abbreviated as XOR or EX-OR. This one is different — it doesn’t just invert a basic gate. The EXCLUSIVE OR gate is designed to produce a ‘1’ output whenever its input signals are dissimilar. That means it compares two input signals — and it compares a maximum of two inputs, no more. If the two inputs have the same value — both ‘0’ or both ‘1’ — the output is ‘0’. If the two inputs have different values — one ‘0’ and one ‘1’ — the output is ‘1’. So the output is ‘1’ only when the inputs are unlike. That’s the exclusive part: it excludes the case where both are ‘1’, unlike a standard OR gate. The representations are shown in Figure 17.6. So to summarise these three gates in one sentence each: NAND gives a ‘1’ unless all inputs are ‘1’; NOR gives a ‘1’ only when all inputs are ‘0’; and EXCLUSIVE OR gives a ‘1’ only when its two inputs are different. These are fundamental building blocks in digital logic, and you’ll see them in everything from aircraft warning systems to autopilot logic.