How to Build a 16 Bit Fibonacci LFSR in Minecraft.
THERE IS a complete nTutorial on how to Build the Shift Register we are working from. This Ciruit nGenerates pseudorandom numbers in minecraft. We Start out with a 16 BIT Serail nOut Shift Register, Shifting Right to Left.

The most commonly used linear nfunction of single bits is XOR. Thus, an LFSR is most often a shift register nwhose input bit is driven by the exclusive-or (XOR) of some bits of the overall nshift register value.

The initial value of the LFSR is called the seed, nand because the operation of the register is deterministic, the stream of values nproduced by the register is completely determined by its current (or previous) nstate. Likewise, because the register has a finite number of possible states, it nmust eventually enter a repeating cycle. However, an LFSR with a well-chosen nfeedback function can produce a sequence of bits which appears random and which nhas a very long cycle.

The 16 Bit Register:
This Shift Register is a ncascade of 1 Wide D Flip-Flops, sharing the same clock, which has the output of nany one but the last flip-flop connected to the "data" input of the next one in nthe chain, resulting in a circuit that shifts by one position, when enabled to ndo so by a transition of the clock input. Video Tutorial link nbelow..

Fibonacci LFSR:
The bit positions that affect the next state nare called the TAPS. [16,14,13,11]. The rightmost bit of the LFSR is called the noutput bit. The taps are XOR'd sequentially with the output bit and then fed nback into the leftmost bit. The sequence of bits in the rightmost position is ncalled the output stream.
The sequence of numbers generated by an LFSR can be nconsidered a binary numeral system just as valid as Gray code or the natural nbinary code.

The arrangement of taps for feedback in an LFSR can be nexpressed in finite field arithmetic as a polynomial mod 2. This means that the ncoefficients of the polynomial must be 1's or 0's. This is called the feedback npolynomial or characteristic polynomial.

Pseudorandomness:
A npseudorandom number generator (PRNG), also known as a deterministic random bit ngenerator (DRBG), is an algorithm for generating a sequence of numbers that napproximates the properties of random numbers. The sequence is not truly random nin that it is completely determined by a relatively small set of initial values, ncalled the PRNG's state, which includes a truly random seed. pseudorandom nnumbers are important in practice for their speed in number generation and their nreproducibility, and they are thus central in applications such as simulations, nin cryptography, and in procedural generation. Good statistical properties are a ncentral requirement for the output of a PRNG, and common classes of suitable nalgorithms include linear congruential generators, lagged Fibonacci generators, nand linear feedback shift registers.

Applications:
generating npseudo-random numbers, pseudo-noise sequences, fast digital counters, and nwhitening sequences, Rave House.

Shift Register Tutorial:
http://www.youtube.com/watch?v=LgAZ5iRsrLM

Linear nFeedback Shift Register:
http://en.wikipedia.org/wiki/Linear_feedback_shift_register