Shift register

Also called: shifter register, shift-register, shifting register, serial shift register

A register whose flip-flops are chained so each one loads its neighbor's value, moving every bit one place along at each clock edge.

A shift register is a register whose flip-flops pass bits along a chain. Each flip-flop's D input is driven by its neighbor's Q, so at every rising edge each bit moves one place.

The first flip-flop's D is the serial input (SI): a new bit enters there each edge.
The last flip-flop's Q is the serial output: its bit leaves at the next edge.

The course's direction convention, with contents written Q3 Q2 Q1 Q0:

Shift right: bits move toward Q0. SI enters Q3; the old Q0 drops out. Wiring: D3 = SI, D2 = Q3, D1 = Q2, D0 = Q1.
Shift left: bits move toward Q3. SI enters Q0; the old Q3 drops out.

Why it works: at an edge, every flip-flop samples its neighbor's value from just before the edge, then all update together. That is why edge triggered flip-flops are essential: with transparent latches a bit could race through several stages in one pulse.

What shift registers are used for:

converting between serial and parallel data (SISO, SIPO, PISO, PIPO),
delay lines,
multiplying and dividing by 2 (shift left, logical shift right, arithmetic shift right),
rotating bits, and simple counters such as the ring counter and johnson counter.

Worked examples

Example

Reading the diagram above

A shift-right chain SI → Q3 → Q2 → Q1, all starting at 0. Rising edges are in slots 2, 4, 6, 8 and 10.

1.
Q3 is a D flip-flop on SI. At the edges SI is 0, 1, 1, 0, 0, so Q3 changes to 1 at slot 4 and back to 0 at slot 8.
2.
Q2 copies Q3's value from just before each edge. At slot 6 Q3 was 1, so Q2 becomes 1. At slot 10 Q3 was 0, so Q2 becomes 0.
3.
Q1 copies Q2 the same way, one edge later: it becomes 1 at slot 8.
4.
Each stage is the previous stage delayed by one clock period.

Example

Tracing contents

A 4-bit shift-right register starts at 1001. The serial input is 1, 1, 0, 1 on edges 1–4.

1.
Edge 1: SI = 1 enters Q3, the rest move right, Q0's 1 drops out: 1100.
2.
Edge 2: SI = 1: 1110.
3.
Edge 3: SI = 0: 0111.
4.
Edge 4: SI = 1: 1011.
5.
Quick method each edge: cross off the rightmost bit and write SI on the left.

Common mistakes

Updating the bits one at a time. Shifting 1011 right with SI = 0 that way smears the 0 across everything; the real answer is 0101, because every flip-flop reads its neighbor's old value.
Putting SI at the wrong end. For shift right it enters Q3; for shift left it enters Q0.
Forgetting that the bit at the far end is lost unless it is fed back.

Practice Shift register

Interactive questions with instant feedback and a worked solution for every wrong answer.

Registers lesson full course

And 17 more in the Registers lesson.

Practice exams

Learn it step by step

Shift register is taught in Registers and Counters.

Registers →Counters →

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