The three multivibrators
One family, three members, distinguished by how many stable states they have.
| Circuit | Stable states | Behaviour |
|---|---|---|
| Bistable (flip-flop) | two | stays where you put it |
| Monostable (one-shot) | one | switches temporarily to an alternate state for a set time, then returns |
| Astable | none | continuously 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
| Gate | Output |
|---|---|
| AND | 1 only if all inputs are 1 |
| OR | 1 if any input is 1 |
| NAND | 0 only if all inputs are 1 |
| NOR | 1 only if all inputs are 0 |
| XOR | 1 if inputs differ |
| XNOR | 0 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
- You need to divide a 4 MHz clock to 250 kHz. How many flip-flops?
- A two-input gate outputs 0 only when both inputs are 1. Which gate?
- Which multivibrator is an oscillator?
Answers
- 4 MHz / 250 kHz = 16, so four flip-flops.
- NAND.
- Astable — no stable state, so it alternates continuously.