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=> Algebraic Curves-Mordell Curve
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=> Algebraic Integer
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=> Algebraic Number Theory
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=> Russian Multiplication
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=> Steffi Problem
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=> Euler's Totient Rule
=> Goodstein Sequence
=> Hereditary Representation
=> Least Significant Bit
=> Midy's Theorem
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=> Negabinary
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=> One-Seventh Ellipse
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Ziyaretçi defteri
 

Least Significant Bit

 
LeastSignificantBit

The value of the 2^0 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, ... (Sloane's A000035). It can be represented as

a(n) = 1/2[1-(-1)^n]
(1)
= 1/2(-1)^n[-1+(-1)^n]
(2)

or

 a(n)=n (mod 2).
(3)

It is also given by the linear recurrence equation

 a(n)=1-a(n-1)
(4)

with a(1)=1 (Wolfram 2002, p. 128).

Similarly, the "most significant bit" is the value of the 2^n bit in an n-bit representation.

 

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