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Unit II Overview: Combinational Circuits and Flip-Flops — Computer Organization and Architecture Notes

Combinational vs Sequential Digital Circuits

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Combinational vs Sequential Comparison

Feature	Combinational	Sequential
Memory	None	Has flip-flops / latches
Feedback	No feedback path	Has feedback (output to input)
Clock	Not required	Usually clock-driven (synchronous)
Output depends on	Current inputs only	Current inputs + current state
Examples	MUX, Decoder, Encoder, Adder, ALU	Counters, Registers, RAM, CPUs
Complexity	Lower	Higher
Analysis method	Truth table, Boolean algebra	State table, state diagram

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Combinational Circuits Overview

Circuit	Function	Inputs → Outputs	Key Application
Multiplexer (MUX)	Select 1 of N data inputs using select lines	2ⁿ data + n select → 1 output	Data routing, function generators
Demultiplexer (DEMUX)	Route 1 input to 1 of N outputs	1 data + n select → 2ⁿ outputs	Data distribution
Encoder	Convert 2ⁿ inputs to n-bit binary code	2ⁿ → n	Keyboard encoding, A/D conversion
Decoder	Convert n-bit binary to 2ⁿ outputs	n → 2ⁿ	Memory address decode, display drivers
Comparator	Compare two n-bit numbers (A=B, A>B, A<B)	2n → 3	Sorting, conditional branches
Adder/ALU	Arithmetic and logic operations	2n + carry → n + carry	CPU arithmetic unit

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Sequential Circuits Overview

Type	Description	Clock	Application
SR Flip-Flop	Set-Reset; basic memory cell	Edge/Level	Status flags
D Flip-Flop	Data; captures input on clock edge	Edge	Registers, pipeline stages
JK Flip-Flop	Universal; no invalid state; toggle mode	Edge	Counters, state machines
T Flip-Flop	Toggle; flips state on T=1	Edge	Binary counters
Register	Group of flip-flops storing n-bit word	Edge	CPU registers, buffers
Counter	Sequential state machine counting clock pulses	Edge	Clocks, timers, address generators

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Study Deep: The Concept of State

A state is a snapshot of all stored values (flip-flop outputs) at a given clock cycle. Sequential circuits implement Finite State Machines (FSMs):

Moore machine: Output depends only on current state
Mealy machine: Output depends on current state AND current inputs (faster response, fewer states)

Every digital system you use — smartphone, CPU, network card — is a collection of FSMs implemented with flip-flops and combinational logic.

📝 Exam Tip: Key distinction: combinational = no memory, output = f(current inputs only); sequential = has memory, output = f(current inputs, current state). CPU internal registers make it fundamentally a sequential circuit.