Linear feedback shift register

Definition

A linear feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. It is commonly used in digital circuits for applications such as pseudorandom number generation and error detection, providing a way to generate sequences of bits that appear random. The connection polynomial of the LFSR determines the sequence generated and can be used to design for testability in digital systems by allowing easier testing and fault isolation.

5 Must Know Facts For Your Next Test

1. LFSRs are widely used in communication systems for scrambling and descrambling signals due to their ability to generate long pseudorandom sequences efficiently.
2. The maximum length of the sequence generated by an LFSR can be calculated using the degree of the characteristic polynomial, which must be primitive for maximum length.
3. LFSRs can be easily implemented in hardware, making them a popular choice for compact designs in digital circuits.
4. They are instrumental in generating test patterns for design verification, helping identify faults by providing predictable output sequences.
5. An LFSR can be reset or initialized to a known state, making it easier to reproduce specific test conditions during testing.

Review Questions

• How does a linear feedback shift register contribute to the testing process in digital design?
  • A linear feedback shift register aids the testing process by generating predictable pseudorandom sequences that can be used as test patterns. This predictability allows engineers to easily identify discrepancies between expected and actual outputs during testing. By using these patterns, they can isolate faults in the circuitry more efficiently, ensuring that each component operates correctly and improving overall system reliability.
• What role does the characteristic polynomial play in determining the functionality and efficiency of an LFSR?
  • The characteristic polynomial of an LFSR determines its feedback connections, which directly influence the sequence of bits generated. If the polynomial is primitive, it enables the LFSR to produce a maximum-length sequence, maximizing the efficiency of the bit generation. This property is vital for applications like scrambling data in communication systems, as it ensures long sequences that enhance security and reduce patterns that could be exploited.
• Evaluate how the design of an LFSR can impact fault detection and isolation in complex digital systems.
  • The design of an LFSR significantly influences fault detection and isolation capabilities within complex digital systems. By integrating an LFSR with specific feedback configurations, engineers can tailor output sequences that target potential weak points in the circuit. This strategic design enables systematic testing where certain faults may produce distinctive output patterns, allowing for quicker identification and remediation of issues within the hardware.

Related terms

Shift Register: A type of sequential circuit that is used to store and manipulate data bits by shifting them in and out on clock pulses.

Feedback Function: A function that combines selected bits from the register to produce the input for the next state, which is crucial for determining the behavior of an LFSR.

Pseudorandom Sequence: A sequence of numbers that only approximates true randomness, often generated by algorithms like those used in LFSRs.