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Hardware/Analogue_and_digital.md
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---
title: Analogue and digital
categories:
- Computer Architecture
- Hardware
tags: [analogue, digital]
---

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Hardware/Binary/Binary_units_of_measurement.md
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---
title: Binary units of measurement
categories:
- Computer Architecture
- Hardware
- Mathematics
tags: [bits, binary]
---
# Binary units of measurement
A single place or symbol in a decimal number is called a **digit**. For example the number 34.3 is a number containing three digits. A digit can be any numeral through 0-9.
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](/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
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. Therefore to express greater complexity we work with sequences of bits. Everytime we increase the binary place value of a binary number we are adding to the sequence and increasing the overall complexity of the number by a factor of 2.
### 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.