A bit has two possible states; a fixed-width unsigned binary word encodes an integer.
Key knowledge
A binary digit takes a value 0 or 1. In an n-bit unsigned positional encoding, bit i contributes bᵢ2ⁱ, with the rightmost bit at i=0. The n-bit word represents an integer from 0 to 2ⁿ−1.
Values and equations
N = Σᵢ₌₀ⁿ⁻¹ bᵢ2ⁱ; 0 ≤ N ≤ 2ⁿ−1
N
Encoded nonnegative integer
n
Positive word length bits
bᵢ
Digit at position i, either 0 or 1
i
Bit position, counted from zero at the right
Conditions and scope
n is a positive integer and bᵢ is 0 or 1.
This is unsigned positional interpretation; signed numbers, text and other data require an explicitly specified encoding.
Stored bit count does not by itself specify Shannon entropy.
Sources · 2
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
Unsigned positional encoding and its representable range.
2026-10-10 · Checked bit positions and the distinction between a bit pattern and its interpretation.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
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