Logic gates are the basic building blocks of digital circuits, computers, calculators, sensors, and control systems. This cheat sheet helps students connect gate symbols, Boolean expressions, and truth tables in one quick reference. It is useful for reading circuit diagrams, predicting outputs, and designing simple digital systems.
Students in grades 9-12 need these skills before moving into electronics, robotics, coding, and engineering design.
Key Facts
- An AND gate outputs 1 only when all inputs are 1, so for two inputs the expression is Y = A AND B.
- An OR gate outputs 1 when at least one input is 1, so for two inputs the expression is Y = A OR B.
- A NOT gate inverts one input, so if Y = NOT A, then input 0 gives output 1 and input 1 gives output 0.
- A NAND gate is the opposite of AND, so Y = NOT(A AND B) and it outputs 0 only when all inputs are 1.
- A NOR gate is the opposite of OR, so Y = NOT(A OR B) and it outputs 1 only when all inputs are 0.
- An XOR gate outputs 1 when the two inputs are different, so for two inputs it is 1 for 01 and 10.
- An XNOR gate outputs 1 when the two inputs are the same, so for two inputs it is 1 for 00 and 11.
- A truth table with n binary inputs has 2^n rows because each input can be either 0 or 1.
Vocabulary
- Logic Gate
- A digital circuit element that takes one or more binary inputs and produces one binary output.
- Binary
- A number system or signal system that uses only two values, usually 0 and 1.
- Boolean Expression
- A symbolic expression that describes a logic circuit using variables and operators such as AND, OR, and NOT.
- Truth Table
- A table that lists every possible input combination and the output produced by a logic circuit.
- Input
- A binary value supplied to a logic gate or circuit before the output is determined.
- Output
- The binary result produced by a logic gate or circuit after applying its logic rule.
Common Mistakes to Avoid
- Confusing OR with XOR is wrong because OR outputs 1 when either or both inputs are 1, while XOR outputs 1 only when the inputs are different.
- Forgetting that NAND and NOR include NOT is wrong because their outputs are the exact opposites of AND and OR.
- Leaving out input combinations in a truth table is wrong because a complete table must include 2^n rows for n inputs.
- Applying NOT to only one variable when parentheses show a group is wrong because NOT(A AND B) means invert the result of the whole AND expression.
- Reading 1 and 0 as ordinary numbers instead of logic states is wrong because in digital logic they represent true and false, high and low, or on and off.
Practice Questions
- 1 For inputs A = 1 and B = 0, find the outputs of AND, OR, NAND, NOR, XOR, and XNOR.
- 2 How many rows are needed in a truth table for a circuit with 4 inputs?
- 3 Complete the output column for Y = NOT(A OR B) for input pairs 00, 01, 10, and 11.
- 4 A safety system should turn on only when two sensors both detect a safe condition. Which basic logic gate best matches this requirement, and why?