Logic Gates

Digital Logic & Microprocessor — Digital Logic, NEC licence examination syllabus (Nepal Engineering Council).

Logic Gates

Seven small decisions that every computer is built from.

What a gate actually is

A gate is a tiny circuit that takes one or two inputs — each a 0 or a 1 — and produces one output, following a fixed rule.

That is genuinely all. The rules are the kind of thing you would state in ordinary conversation:

🚪 The rules, in plain words

AND"Both of them." The alarm sounds if the door is open AND the system is armed.

OR"Either one." The light comes on if the hall switch OR the landing switch is pressed.

NOT"The opposite." If the tank is not full, run the pump.

Everything else is a combination. NAND is AND followed by NOT. NOR is OR followed by NOT. You do not learn seven separate things — you learn three, and then "then invert it".

The symbols, and how to remember them

💡 Two shapes and one rule cover almost everything. Flat back = AND. Curved back = OR. And a small circle anywhere on an output always means "then invert". Once you see the circle as an inverter you never confuse NAND with AND again.

The truth table, which is just a list of every case

With two inputs there are only four possible situations, so you can simply write all of them down. That list is the truth table, and it is a complete description — there is nothing about the gate it leaves out.

A B │ AND OR NAND NOR XOR ───────┼────────────────────────────── 0 0 │ 0 0 1 1 0 0 1 │ 0 1 1 0 1 1 0 │ 0 1 1 0 1 1 1 │ 1 1 0 0 0

💡 Read the NAND column and compare it with AND — every value is flipped. Same for NOR against OR. Seeing that in the table is worth more than memorising four separate columns.

XOR: the useful odd one

XOR means "one or the other, but not both." It answers "are these two different?" — output 1 when the inputs disagree, 0 when they match.

That makes it the natural gate for addition. In binary, 0+1 and 1+0 both give 1, while 1+1 gives 0 with a carry. That is precisely XOR's column, which is why every adder you meet later starts with one.

Why NAND is called universal

Any circuit whatsoever can be built from NAND gates alone. Not "most" — any.

NOT from NAND: tie both inputs together AND from NAND: a NAND, then another as an inverter OR from NAND: invert both inputs, then NAND them

💡 This matters commercially, not just theoretically. A factory that makes only NAND chips can build anything, so NAND is cheap and available — which is why real designs are often converted into NAND-only form before manufacture.

Exam notes

📝 What gets asked

Draw and complete a truth tableGiven a gate or a small circuit. Always list inputs in counting order — 00, 01, 10, 11 — so you cannot skip a row.

Build X using only NANDA standard question. Know the three constructions above.

Identify from a symbolCheck the back first (flat or curved), then look for the circle.

Syllabus points

AND, OR, NOT, NAND, NOR, XOR, XNOR
Universal gates

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