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Introduction to Programmable PRNG: Linear Feedback Shift Register (LFSR)

Explore the fundamentals of a Programmable Random Number Generator (PRNG) using a Linear Feedback Shift Register (LFSR) technique. Learn about the structure, connection polynomial, initial state, and recursion in this guide.

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Introduction to Programmable PRNG: Linear Feedback Shift Register (LFSR)

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  1. Introduction to Experiment 5 Programmable PRNG

  2. 4 D Q ena coeff 8 4 D Q 2 ena PRNG 0 8 1 output 2 seed 4 D Q 3 ena 2 address 4 data 4 D Q ena write clk load reset

  3. seed(7..4) coeff(7..4) coeff(3..0) seed(3..0) PRNG 7..4 PRNG 3..0 1 0 coeff(7..4)="0000" clk load 2 PRNG clk load output

  4. Linear Feedback Shift Register (LFSR) Each stage = D flip-flop  L, C(D)  Length Connection polynomial, C(D) C(D) = 1 + c1D + c2D2 + . . . + cLDL

  5. Sj-1 Sj-2 Sj-(L-1) Sj-L Initial state [sL-1, sL-2, . . . , s1, s0] LSFR recursion: sj = c1sj-1 c2sj-2 . . .  cL-1sj-(L-1) cLsj-L for j  L

  6. Example of LFSR  4, 1+D+D4 Length Connection polynomial, C(D) C(D) = 1 + 1D + 0D2 + 0D3 +1D4 c1=1 c2=0 c4=1 c3=0

  7. LFSR State Sequence s4 s3 s2 s1 s0 s4 = c1s3c2s2 c3s1  c4s0 = s3 s0

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