Registers and shift registers

Holding a whole number

In the last stage you met the D flip-flop. Here is the one-line reminder: it has a data input D, a clock input, and an output Q. At the moment the clock rises, it copies whatever is on D to Q, and then it holds that value, ignoring D, until the next rising edge. One flip-flop holds one bit.

A number is several bits, so to hold a number you need several flip-flops. Put four of them side by side, give every one the same clock, and feed each one its own bit of the number. On the clock edge all four copy their inputs at the same moment, and between edges the number just sits there. That is a register: a row of D flip-flops sharing one clock, holding one bit each and a whole value together.

Most registers also have a load control. When load is 1, the flip-flops take the new value on the next edge. When load is 0, each flip-flop's D input is wired back from its own Q, so the edge copies the old value over itself and nothing changes. That is what lets a register keep a number for as long as you like while the clock keeps ticking: a register either loads or holds, and the load line says which.

Sliding the bits along

Now wire the flip-flops differently. Instead of giving each one its own input, connect the Q of the first to the D of the second, the Q of the second to the D of the third, and so on down the row. Only the first flip-flop has an outside input. On every clock edge, each flip-flop copies its neighbour's output, so every bit moves one place along the row. This is a shift register, and each flip-flop in it is called a stage.

Try it. Set the input bit, press the clock, and watch the bit enter at Q0 and walk towards Q3. Feed in a few 1s and 0s and the whole pattern travels along, one place per press. The table under the lamps is the history: read a column downwards and you see one bit travelling; read a row across and you see what the register held at that moment.

Because the data goes in one bit per clock, this is called serial input: the bits arrive in a series, one after another, on a single wire. A value that is presented all at once, one wire per bit, is called parallel. A shift register can have either kind of input and either kind of output, which gives four kinds by name:

• Serial in, serial out (SISO): one bit in per clock, one bit out per clock, from the last stage. A delay line: whatever goes in comes out a fixed number of clocks later.
• Serial in, parallel out (SIPO): one bit in per clock, then read all the stages at once. This turns one wire into many, which is how a byte arriving down a single wire ends up on eight.
• Parallel in, serial out (PISO): load a whole word at once, then clock it out one bit at a time down one wire. Sending, the reverse of the one above.
• Parallel in, parallel out (PIPO): everything at once in and out. That is just the ordinary register from the top of this lesson.

What shifting does to a number

Read the widget's stages as a number with Q3 as the most significant bit, as the line under the lamps does. Data entering at Q0 and moving towards Q3 is then a shift left: every bit moves into the column with twice the weight. If the bit coming in on the right is a 0, the number doubles.

What to remember

• A register is n D flip-flops sharing one clock; it holds an n bit value and either loads or holds on each edge.
• A shift register wires each stage's output to the next stage's input, so every bit moves one place per clock edge.
• Serial means one bit per clock on one wire; parallel means all bits at once. The four kinds are SISO, SIPO, PISO and PIPO.
• Shifting left with a 0 coming in doubles the number; shifting right halves it.
• The bit pushed off the end is lost unless something else catches it.