Base notation

Also called: base subscript, subscript notation, 0x prefix, hex prefix

Ways of marking which base a number is written in: a subscript like 1011₂ or 2F₁₆, or a prefix in code such as 0x for hex and 0b for binary.

The string 101 could mean five, one hundred and one, or two hundred and fifty-seven, depending on the base. Base notation removes the doubt.

Subscripts, used in this course and most textbooks: write the base, in decimal, after the number. 101₂ = 5, 101₁₀ = 101, 101₁₆ = 257.

Prefixes, used in programming languages:

0x for hex: 0x2F = 47
0b for binary: 0b1011 = 11
0o for octal in some languages: 0o17 = 15

Other markers you may see: a trailing h for hex in some assembly languages (2Fh), and # before web colors (#FF8800), which are hex.

When the base is obvious from context, such as a bit pattern in a two's complement question, the subscript is often left off. When in doubt, check before you convert. 0x10 is sixteen, not ten.

16¹

16⁰

Worked example

Example

Same digits, different bases

The digits 11 under four different markers.

1.
11₂ = 2 + 1 = 3.
2.
11₈ = 8 + 1 = 9.
3.
11₁₀ = 11.
4.
11₁₆ = 0x11 = 16 + 1 = 17.
5.
The digits match but the values don't, so the marker matters.

Common mistakes

Reading 0x10 as ten.
Treating the subscript as part of the number's value.
Writing a base in its own base. Every base is 10 in itself, so subscripts are always decimal: ₁₆, not ₁₀, for hex.

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Base notation is taught in Number Systems.

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