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Radiocert

Digital Circuits and Logic

Name each logic gate by its truth table, tell the three multivibrators apart, and compute how many flip-flops a given division ratio needs.

5:16
10 min readE7AComponents & CircuitsadvancedDraft

The three multivibrators

One family, three members, distinguished by how many stable states they have.

CircuitStable statesBehaviour
Bistable (flip-flop)twostays where you put it
Monostable (one-shot)oneswitches temporarily to an alternate state for a set time, then returns
Astablenonecontinuously alternates between two states — an oscillator

Which circuit is bistable?

A flip-flop.

The names say it: bi-stable has two stable states, mono-stable has one, a-stable has none.

Dividing frequency

Which of the following can divide the frequency of a pulse train by 2?

A flip-flop.

A flip-flop changes state on each input pulse, so it takes two input pulses to produce one complete output cycle — division by two.

How many flip-flops are required to divide a signal frequency by 16?

4.

Each stage halves, so n stages divide by 2ⁿ. 2⁴ = 16, so four. Same arithmetic as the 3-bit counter in the General track, and the same as the decibel doublings — powers of two keep appearing.

What is the function of a decade counter?

It produces one output pulse for every 10 input pulses.

Division by ten, which needs four flip-flops plus logic to reset at ten rather than sixteen.

The gates

GateOutput
AND1 only if all inputs are 1
OR1 if any input is 1
NAND0 only if all inputs are 1
NOR1 only if all inputs are 0
XOR1 if inputs differ
XNOR0 if one and only one input is 1

Two of these are worth reading twice.

NAND is AND with the output inverted, so the pool’s phrasing — “produces a 0 at its output only if all inputs are 1” — is exactly AND’s condition with the answer flipped.

XNOR is XOR inverted: it outputs 1 when the inputs match. The pool states it the other way round — “produces a 0 if one and only one of its inputs is 1” — which is the same statement, since exactly one input high is precisely the case where they differ.

Truth tables and logic convention

What is a truth table?

A list of inputs and corresponding outputs for a digital device.

The complete specification of a combinational circuit: every input combination, and what comes out. Nothing about timing or voltage — just the logic.

What does “positive logic” mean in reference to logic devices?

High voltage represents a 1, low voltage a 0.

The intuitive convention, and the usual one. Negative logic inverts it, and exists because some technologies switch more efficiently pulling down than pulling up. Worth knowing that the convention is a choice, because a datasheet using the other one will otherwise read as nonsense.

Check yourself

  1. You need to divide a 4 MHz clock to 250 kHz. How many flip-flops?
  2. A two-input gate outputs 0 only when both inputs are 1. Which gate?
  3. Which multivibrator is an oscillator?
Answers
  1. 4 MHz / 250 kHz = 16, so four flip-flops.
  2. NAND.
  3. Astable — no stable state, so it alternates continuously.

Pool questions this lesson answers

11 questions from 2024-2028 Amateur Extra (Element 4). Drill them in targeted practice.

E7A01 · E7A02 · E7A03 · E7A04 · E7A05 · E7A06 · E7A07 · E7A08 · E7A09 · E7A10 · E7A11

Sources

  • pool E7A