How it works
Combinational circuits produce outputs that depend only on current inputs, with no memory. A multiplexer (MUX) selects one of 2ⁿ inputs using n select lines; the 74HC151 is 8:1 with 3 select lines. A demultiplexer (DEMUX) routes one input to one of 2ⁿ outputs; 74HC138 is a 3-to-8 decoder/DEMUX. A decoder activates one output corresponding to the binary input code: 2-to-4 decoder has 4 outputs, only one high at a time. An encoder performs the reverse — 8-to-3 priority encoder 74HC148 outputs the binary code of the highest-priority active input. A digital comparator like the 74HC85 compares two 4-bit numbers and outputs three signals: A>B, A=B, A<B. These circuits are designed by writing the truth table, deriving Boolean expressions, and simplifying with K-maps.
Key points to remember
A 2ⁿ:1 MUX requires n select lines and can implement any n-variable Boolean function by connecting input data lines to 0 or 1 according to the truth table — no additional gates needed. The 74HC138 decoder/DEMUX has active-low outputs; all outputs are high except the selected one, which goes low. BCD-to-seven-segment decoder (7447) converts 4-bit BCD to seven output signals driving individual LED segments a–g. Propagation delay through combinational circuits causes glitches (hazards): static-1 hazard occurs when output momentarily goes 0 during an input transition even though it should remain 1, correctable by adding a consensus term. Priority encoders handle multiple simultaneous active inputs by responding only to the highest-priority one.
Exam tip
The examiner always asks you to implement a Boolean function using a MUX — write the truth table, assign data inputs D0–D7 according to function output for each minterm, connect select lines to input variables, and draw the connection diagram.