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SISO register with 1101 data

Short answer

Data 1101 is loaded LSB-first into a 4-bit SISO register over four clocks, storing 1101 (QA=1,QB=1,QC=0,QD=1) after clock 4. Serial output at QD produces 1,0,1,1 over clocks 5–8. Loading takes 4 pulses; reading out takes 4 pulses, with the first bit appearing at clock 5.

Explain the operation of 4 bit serial-in-serial out (SISO) register with timing diagram for the given data pattern 1101.

A 4-bit serial-in serial-out (SISO) shift register is four D flip-flops connected in a chain with a common clock. Data enters one bit per clock at the first flip-flop and comes out one bit per clock from the last flip-flop.

Circuit

 Din  +-----+   +-----+   +-----+   +-----+
 ---->|D  QA|-->|D  QB|-->|D  QC|-->|D  QD|--> Dout
      |>    |   |>    |   |>    |   |>    |
      +-----+   +-----+   +-----+   +-----+
         ^         ^         ^         ^
 CLK ----+---------+---------+---------+

Data enters FF-A only and leaves from FF-D only. At each rising edge: QA←Din, QB←QA, QC←QB, QD←QCQA \leftarrow D_{in},\ QB \leftarrow QA,\ QC \leftarrow QB,\ QD \leftarrow QC.

Operation with data 1101

The register is cleared to 0000 first. The data is entered LSB first: serial input = 1, 0, 1, 1 at clocks 1 to 4, then 0s.

CLKSerial inQAQBQCQD (out)
0 (initial)-0000
111000
200100
311010
411101
500110
600011
700001
800000
  • Storing (clocks 1 to 4): after clock 4, QA QB QC QD = 1101, i.e. 1101 is held with QA as MSB.
  • Retrieving (serial out at QD): the output after clocks 4, 5, 6, 7 is 1, 0, 1, 1, which is 1101 read LSB first. After clock 8 the register is empty again.
  • A 4-bit SISO register needs 4 clocks to load and 4 clocks to empty (3 more clocks after the first bit appears).

Timing diagram

       1   2   3   4   5   6   7   8
CLK   _|‾|_|‾|_|‾|_|‾|_|‾|_|‾|_|‾|_|‾|
Din   ‾‾‾|___|‾‾‾‾‾‾‾|________________
QA    _|‾‾‾|___|‾‾‾‾‾‾‾|______________
QB    _____|‾‾‾|___|‾‾‾‾‾‾‾|__________
QC    _________|‾‾‾|___|‾‾‾‾‾‾‾|______
QD    _____________|‾‾‾|___|‾‾‾‾‾‾‾|__

Each Q waveform is the previous one delayed by one clock period.

Uses: delaying a serial signal by 4 clock periods and serial data transfer.

✓ Answer checked by Claude Opus 5.5 (high effort)

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