Generate 5th order linear recursive sequence using shift registers using the primitive polynomial 1+X^2+x^5

Expert Solution

Question

Generate 5th order linear recursive sequence using shift registers using the primitive polynomial 1+x²+x⁵

Sol:

Given polynomial is 1+x²+x⁵

The synchronous sequential circuit should contain a 5 bit shift register and an XOR gate feedback configuration.A total of 32 possible states are there for a sequential circuit having 5 flip flops, but the circuit should not become all zeros as this condition will never change and it must be avoided.

The sequence states are completely determined by the starting state and the feedback connections through the XOR gate.

The maximum sequence length = 2^N-1 where N is the number of flipflops.

In this case the maximum length sequence will be 31.

The feedback loop connects the shift register output back to the input .Here only one flip-flop output feeds an XOR gate while the others are not connected.

Shift register diagram corresponding to polynomial 1+x²+x⁵ is shown below:

venereology answered 1 month ago

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