E7A

Digital logic and flip-flops

Read truth tables for logic gates, and explain how flip-flops and counters divide a frequency.

11 pool questions1 on the exam

Syllabus: Digital circuits: digital circuit principles and logic circuits; classes of logic elements; positive and negative logic; frequency dividers; truth tables

A truth table says what a gate does

A truth table lists every input combination of a digital device and the output it gives. Learn the plain gates, then flip them for the "N" versions.

A truth table lists every input combination and the output it gives. Pick A and B to light a row.

Gate	Output is 1 when
OR	any input is 1
NAND	NOT all inputs are 1 (0 only if all are 1)
XNOR	the two inputs are the same (0 if exactly one is 1)

RememberNAND and XNOR are AND and XOR with the output flipped.

Positive logic: high voltage is 1

Logic is just a naming rule for two voltages. In positive logic, the high voltage is 1 and the low voltage is 0. Negative logic swaps the names.

Same wire, same voltages. Only the naming rule changes.

RememberPositive logic: high = 1, low = 0.

A flip-flop holds a state and halves a frequency

A flip-flop has two stable states (bistable) and holds one until a clock edge flips it. Wired to toggle on every clock pulse, it gives one output cycle for every two input cycles: ÷2.

Each flip-flop halves the frequency. 4 flip-flops = ÷16.

Chain them: each stage halves again, so N flip-flops divide by 2ᴺ. Divide by 16 = 2⁴ needs 4.

RememberN flip-flops = ÷2ᴺ. Bistable = flip-flop.

A decade counter divides by 10

A decade counter counts input pulses 0 to 9, then wraps to 0 and puts out one pulse per 10 inputs. It counts. It does not drive a display; a decoder turns a binary number into the seven-segment pattern.

Ten pulses in, one pulse out. It counts. A decoder is a different part.

RememberCounter: 10 pulses in, 1 out. Decoder: binary in, display pattern out.

Bistable, monostable, astable: how many stable states?

Count the stable states. Astable has none, so it free-runs as an oscillator with no clock. Monostable has one: a trigger sends it to the other state for a set time, then it returns.

Bi = two stable states. Mono = one stable state. A = none: it free-runs.

RememberAstable = free-running square wave. Monostable = one timed pulse per trigger.

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