A Binary Polynomial is a polynomial with coefficients from the binary field , for example X^3+X+1. Every sequence of bits can be
represented by a binary polynomial. The sequence 101011, for example,
can be represented by the polynomial:
X^5+X^3+X^1+X^0 =
X^5+X^3+X+1.
As seen by the example, the rightmost bit of the sequence represents the lowest degree of the polynomial (degree zero). Logical left shift of i bits can be represented by multiplying the polynomial by X^i.