Shift Registers
A register that moves its bits one position each clock — left, right, or in a ring.
Description
A register whose bits shift one place per clock, optionally taking a serial input. It converts between serial and parallel data and builds delays and sequence generators. Each flip-flop's output feeds the next flip-flop's input; a serial bit enters one end.
- SISO — serial in, serial out (a delay line).
- SIPO — serial in, parallel out (deserializer).
- PISO — parallel in, serial out (serializer).
- PIPO — parallel in, parallel out (a normal load register).
- Ring: the output wraps straight back to the input — n distinct states.
- Johnson (twisted ring): the complemented output wraps back — 2n states.
- What: A register whose bits shift one place per clock, optionally taking a serial input.
- Why: It converts between serial and parallel data and builds delays and sequence generators.
- How: Each flip-flop's output feeds the next flip-flop's input; a serial bit enters one end.
- Where: UART/SPI serializers, LFSRs, delay lines, ring/Johnson counters.
At a glance
What
A register whose bits shift one place per clock, optionally taking a serial input.
Why
It converts between serial and parallel data and builds delays and sequence generators.
How
Each flip-flop's output feeds the next flip-flop's input; a serial bit enters one end.
Where
UART/SPI serializers, LFSRs, delay lines, ring/Johnson counters.
When
Whenever data must move serially or be delayed by clock cycles.
Think of it like…
A bucket brigade: each clock, every person passes their bucket to the next. A ring brigade forms a circle so buckets keep going around.
Four data paths
- SISO — serial in, serial out (a delay line).
- SIPO — serial in, parallel out (deserializer).
- PISO — parallel in, serial out (serializer).
- PIPO — parallel in, parallel out (a normal load register).
Ring vs Johnson
- Ring: the output wraps straight back to the input — n distinct states.
- Johnson (twisted ring): the complemented output wraps back — 2n states.
Counter from shift register
| Type | Feedback | States (n FFs) |
|---|---|---|
| Ring | Qlast → Qfirst | n |
| Johnson | Qlast′ → Qfirst | 2n |
Black-box view
Inputs on the left → outputs on the right · particles show signal direction
Shift, ring, and Johnson modes
▶ live simulatorPick a mode, then press Clock ▲ to shift and trace each bit.
Real-world applications
The 5 Whys
- 1
Why shift registers? To move data serially and convert serial↔parallel.
- 2
Why serial transfer? It needs only one wire instead of n.
- 3
Why ring/Johnson? They make cheap, glitch-free counters.
- 4
Why Johnson over ring? Twice the states for the same flip-flops.
- 5
Root cause: chaining flip-flops output-to-input turns storage into controlled motion of bits.
Cheat sheet
Working principle
- Each flip-flop's output feeds the next flip-flop's input; a serial bit enters one end.
- A register whose bits shift one place per clock, optionally taking a serial input.
Formulas & Boolean expressions
- Right shift: Qᵢ⁺ = Qᵢ₊₁ (serial-in → MSB)
- Ring states = n, Johnson states = 2n
Key facts
- SISO — serial in, serial out (a delay line).
- Ring: the output wraps straight back to the input — n distinct states.
Why it exists
- Root cause: chaining flip-flops output-to-input turns storage into controlled motion of bits.