Combinational logic building blocks are digital circuits whose outputs depend only on the current inputs. This cheat sheet helps engineering students recognize common blocks, read their symbols and truth tables, and predict their outputs. These blocks are the foundation for arithmetic units, control circuits, data routing, and digital decision making.
Knowing them makes larger digital systems easier to design and debug.
The most important idea is that each block implements a Boolean function using 0 and 1 logic levels. Gates perform basic operations such as AND, OR, NOT, NAND, NOR, XOR, and XNOR. Larger blocks such as multiplexers, decoders, encoders, adders, and comparators combine gates into reusable modules.
Truth tables, Boolean expressions, and enable inputs are the main tools for describing how each block behaves.
Key Facts
- A combinational circuit has outputs determined only by present inputs, so output = f(current inputs).
- The basic AND rule is Y = A AND B, which equals 1 only when A = 1 and B = 1.
- The basic OR rule is Y = A OR B, which equals 1 when A = 1, B = 1, or both are 1.
- The NOT rule is Y = NOT A, so an input of 0 gives 1 and an input of 1 gives 0.
- A 2-to-1 multiplexer follows Y = NOT S AND D0 OR S AND D1, so select S chooses which data input reaches the output.
- A decoder with n inputs can activate up to 2^n output lines, usually with exactly one output active for each input code.
- A half adder has Sum = A XOR B and Carry = A AND B.
- A full adder has Sum = A XOR B XOR Cin and Cout = AB OR A Cin OR B Cin.
Vocabulary
- Combinational logic
- A type of digital logic where outputs depend only on the current input values, not on stored past values.
- Truth table
- A table that lists every possible input combination and the output produced for each combination.
- Multiplexer
- A digital selector circuit that routes one of several data inputs to a single output based on select inputs.
- Decoder
- A circuit that converts an n-bit binary input code into one active output among up to 2^n outputs.
- Encoder
- A circuit that converts one active input line into a binary output code.
- Propagation delay
- The time it takes for a change at a circuit input to cause the correct change at the output.
Common Mistakes to Avoid
- Confusing combinational logic with sequential logic is wrong because combinational outputs do not depend on memory, clocks, or previous states.
- Treating XOR as the same as OR is wrong because XOR is 1 only when the inputs are different, while OR is also 1 when both inputs are 1.
- Ignoring enable inputs is wrong because a disabled decoder, multiplexer, or buffer may force outputs inactive or high impedance regardless of data inputs.
- Forgetting carry-in on a full adder is wrong because Sum = A XOR B XOR Cin and Cout can change when Cin changes.
- Assuming active-low signals behave like active-high signals is wrong because a bubble or overbar means the signal is asserted when its value is 0.
Practice Questions
- 1 For a 2-input XOR gate, find Y when A = 1 and B = 0.
- 2 A 2-to-1 multiplexer has D0 = 0, D1 = 1, and S = 1. What is the output Y?
- 3 A full adder has A = 1, B = 1, and Cin = 0. Find Sum and Cout.
- 4 Explain why a decoder is useful when a processor needs to select exactly one memory chip from several chips.