10 min readConcept sheetSection A MCQ (1 mark) and objective (2 marks, two parts, often a truth table to complete); Section B very short answer (2 marks) on a gate's symbol and truth table; also a NEET favourite

Logic gates: AND, OR and NOT

Digital signals are 0 or 1. AND gives 1 only when all inputs are 1, OR when any input is 1, and NOT inverts.

AND gateY = A·B (A AND B): the output is 1 only when both inputs are 1

OR gateY = A + B (A OR B): the output is 1 when either input, or both, is 1

NOT gateY = Ā (NOT A): the output is the opposite of the input

Logic levelsUsually 0 V stands for 0 and 5 V for 1

Digital signals

A continuous signal can take any value in a range, like the voltage from a microphone. A discrete signal has values only at certain instants. A digital signal takes only a few fixed values, usually two: 0 and 1, called bits. Typically 0 V means 0 and 5 V means 1. The levels are far apart, so noise of up to about 2 V does not change a bit. Circuits that work on bits are logic gates. They follow Boolean algebra, in which A × 0 = 0 and A + 1 = 1.

Truth tables of AND and OR

A	B	AND: Y = A·B	OR: Y = A + B
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	1

Truth table of NOT

A	NOT: Y = Ā
0	1
1	0

Making the gates with switches, diodes and a transistor

ANDSwitches in series with a bulb: the bulb (Y) glows only if A and B are both ON. Diode version: two diodes with anodes joined, fed from +5 V through a 5 kΩ resistor; inputs at the cathodes, output at the anodes. Any input at 0 V makes its diode conduct, so the output falls to about 0.7 V (logic 0).

ORSwitches in parallel: the bulb glows if A or B, or both, is ON. Diode version: two diodes with cathodes joined and earthed through a 5 kΩ resistor; inputs at the anodes, output at the cathodes. Any input at 5 V makes its diode conduct, giving about 5 V (logic 1).

NOTUse the transistor switch. Input 0 cuts the transistor off, so the output is VCC, logic 1. Input 1 saturates it, so the output is near 0 V, logic 0.

How to draw the symbols

AND: a D shape, with a flat back carrying inputs A and B and a curved front giving output Y.
OR: a shield or arrowhead shape, with a curved back carrying inputs A and B and a pointed front giving output Y.
NOT: a triangle pointing right with a small circle (bubble) at its tip. Input A, output Y = Ā.
Write the Boolean expression under each symbol and draw its truth table beside it.

Worked example: following a gate circuit

Problem

Inputs A and B go into an AND gate. Its output and a third input C go into an OR gate, so Y = A·B + C. Find Y for (a) A = 1, B = 0, C = 0; (b) A = 1, B = 1, C = 0; (c) A = 0, B = 0, C = 1.

Working

(a) A·B = 1·0 = 0, so Y = 0 + 0 = 0.
(b) A·B = 1·1 = 1, so Y = 1 + 0 = 1.
(c) A·B = 0·0 = 0, so Y = 0 + 1 = 1. (Remember that A + 1 = 1.)

Answer

(a) 0; (b) 1; (c) 1

In real life

A washing machine starts only if the door is shut AND the start button is pressed: an AND gate. A car's inside light comes on if the driver's door OR the passenger's door is open: an OR gate.

Exam angle

2 marks: “Draw the logic symbol and write the truth table of a two-input AND gate. How can it be shown with two switches?” D-shaped symbol, Y = A·B. Truth table: 00 gives 0, 01 gives 0, 10 gives 0, 11 gives 1. Two switches in series with a bulb: it glows only if both are ON.

2 marks: “Draw the symbol of a NOT gate and give its truth table. Which transistor circuit acts as a NOT gate?” A triangle with a bubble; A = 0 gives Y = 1 and A = 1 gives Y = 0. The transistor switch: a high input saturates it, so the output is low.

1 marks: “Write the Boolean expression for a two-input OR gate.” Y = A + B.

Remember it

AND needs All, OR needs One, NOT says the Opposite.