2.5 KiB
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| Binary units of measurement |
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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.
We can think of how much data can be stored in a number in terms of the total number of unique arrangemnets of bits or digits. With this in mind, compare a two digit digital number to a two 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 2^{10} (1024):
With the binary number we have 2^{2} (4), giving us far fewer possible unique states. They are so few we can easily list them:
00
01
10
11
Bytes
In order to express larger binary numbers and 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.
A byte allows for a complexity of up to 256 possible states: 2^{8} = 256
Metric units: kilobytes, megabytes etc
Having established that the core quantity of information is the byte, the convention is to apply the standard metric prefixes to the byte to establish units:
| Prefix | Symbol | Expression as exponent | Expression as decimal value | English word |
|---|---|---|---|---|
| Terra- | T | 10^12 |
1,000,000,000,000 | trillion |
| Giga- | G | 10^9 |
1,000,000,000 | billion |
| Mega- | M | 10^6 |
1,000,000 | million |
| Kilo- | k | 10^3 |
1,000 | thousand |
Hence 2MB is two million bytes, 4kb is four thousand bytes etc.