Least Significant Bit

The value of the  bit in a binary number. For the sequence of numbers 1, 2, 3, 4, ..., the least significant bits are therefore the alternating sequence 1, 0, 1, 0, 1, 0, ... (OEIS A000035). It can be represented as

			(1)
			(2)

or

(3)

It is also given by the linear recurrence equation

(4)

with  (Wolfram 2002, p. 128).

Analogously, the "most significant bit" is the value of the  bit in an -bit representation.

The least significant bit has Lambert series

(5)

where  is a q-polygamma function.

REFERENCES:

Sloane, N. J. A. Sequence A000035/M0001 in "The On-Line Encyclopedia of Integer Sequences."

Whitford, A. K. "Binet's Formula Generalized." Fib. Quart. 15, 21, 24, and 29, 1977.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 128, 2002.