Introduction
A combinational circuit is a digital circuit whose output at any instant depends only on the present combination of inputs — it has no memory of past inputs. This is the opposite of a sequential circuit, which stores state (using flip-flops) and depends on both present inputs and past history.
Three combinational building blocks appear again and again in exams for BCS, Bank IT and IT-officer posts: the adder (the arithmetic heart of every CPU/ALU), the multiplexer / MUX (a data selector), and the decoder (an address / code translator). If you master how each is built from basic gates, how many inputs/outputs/select lines each has, and how to use one to implement Boolean functions, you can answer almost every objective question on this chapter.
This lesson builds each device from first principles: truth table → Boolean equation → gate circuit → applications.
Learning Objectives
After studying this lesson you should be able to:
- Distinguish combinational circuits from sequential circuits.
- Derive and draw the half adder and full adder, and build a ripple-carry adder and a subtractor.
- Explain and design multiplexers (2:1, 4:1, 8:1), expand them with MUX trees, and use a MUX to realise any Boolean function.
- Explain and design decoders (2:4, 3:8), use an enable line, and implement functions with a decoder + OR gate.
- Relate encoders and demultiplexers to the above.
- Compute the number of select lines, data lines and outputs for any size of MUX/decoder.
- Solve exam-style numerical and design problems quickly.