eolas/Hardware/Binary/Binary_units_of_measurement.md

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---
title: Binary units of measurement
categories:
- Hardware
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- Mathematics
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tags: [bits, binary]
---
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# Binary units of measurement
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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.
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The equivalent entity in the [binary number system](/Hardware/Binary/The_binary_number_system.md) 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
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### 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.
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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:
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```
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00
01
10
11
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```
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### Bytes
In order to express larger binary numbers and greater complexity we work with sequences of bits.
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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.
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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](/Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md) 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.