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Understanding Pseudo-Random Bit Generation Using Linear Feedback Shift Register

This demonstration showcases the generation of pseudo-random bits utilizing a Linear Feedback Shift Register algorithm. Starting with an initial seed value, the LFSR generates a sequence of bits according to preset rules, providing seemingly random output. The XOR truth tables demonstrate the bitwise operations involved in the process, leading to a string of pseudo-random bits: 11001001...

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Understanding Pseudo-Random Bit Generation Using Linear Feedback Shift Register

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  1. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 "seed" = initial contents 1

  2. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 2

  3. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 3

  4. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 ^ Time 1 1 1 0 1 0 0 0 0 1 0 XOR Truth Table x 0 0 1 1 y 0 1 0 1 x ^ y 0 1 1 0 4

  5. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 ^ Time 1 1 1 0 1 0 0 0 0 1 0 1 XOR Truth Table x 0 0 1 1 y 0 1 0 1 x ^ y 0 1 1 0 5

  6. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 XOR Truth Table x 0 0 1 1 y 0 1 0 1 x ^ y 0 1 1 0 6

  7. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 XOR Truth Table x 0 0 1 1 y 0 1 0 1 x ^ y 0 1 1 0 7

  8. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 XOR Truth Table x 0 0 1 1 y 0 1 0 1 x ^ y 0 1 1 0 8

  9. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 Time 5 0 0 0 0 1 0 1 1 0 0 1 9

  10. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 Time 5 0 0 0 0 1 0 1 1 0 0 1 Time 6 0 0 0 1 0 1 1 0 0 1 0 10

  11. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 Time 5 0 0 0 0 1 0 1 1 0 0 1 Time 6 0 0 0 1 0 1 1 0 0 1 0 Time 7 0 0 1 0 1 1 0 0 1 0 0 11

  12. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 Time 5 0 0 0 0 1 0 1 1 0 0 1 Time 6 0 0 0 1 0 1 1 0 0 1 0 Time 7 0 0 1 0 1 1 0 0 1 0 0 Time 8 0 1 0 1 1 0 0 1 0 0 1 12

  13. Linear Feedback Shift Register Demo Time 0 0 1 1 0 1 0 0 0 0 1 0 Time 1 1 1 0 1 0 0 0 0 1 0 1 Time 2 1 0 1 0 0 0 0 1 0 1 1 Time 3 0 1 0 0 0 0 1 0 1 1 0 Time 4 1 0 0 0 0 1 0 1 1 0 0 Time 5 0 0 0 0 1 0 1 1 0 0 1 Time 6 0 0 0 1 0 1 1 0 0 1 0 Time 7 0 0 1 0 1 1 0 0 1 0 0 Time 8 0 1 0 1 1 0 0 1 0 0 1 pseudo-random bits: 11001001… 13

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