eolas/Hardware/Binary/Binary_units_of_measurement.md
2022-10-03 10:30:05 +01:00

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Binary units of measurement
Hardware
Mathematics
bits
binary

Binary units of measurement

A single place or symbol in a decimal number is called a digit. For example the number 343 is a number containing three digits. A digit can be any numeral through 0-9.

The equivalent entity in the binary number system is the bit. For example the binary number 110 has three bits. A bit can only have one of two values in contrast to a digit which can have one of ten values: 0 or 1.

Sequences of bits

Informational complexity

The informational complexity of digit is much larger than a bit: it can represent one of 10 states whereas a bit can only represent one of two states.

Consider how much data can be stored in a three digit digital number compared to a three bit binary number. For the decimal number each digit can represent one of ten states, hence the total number of unique states is equal to 3^{10} (59049):

001
002
003
...
010
011
012
013
...

With the binary number we have 3^{10} (59049) Therefore to express greater complexity we work with sequences of bits.

The standard base sequence of bits is called a byte. This is a binary number comprising eight bits. For example the number 11001110 is a byte equivalent to 206 in decimal.

Every time we add a bit to the sequence of bits comprising a binary number we increase complexity of the number by a factor of 2, i.e. 1, 2, 4, 8, 16, 32, 64, 128 etc.