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19
Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md
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@ -8,15 +8,16 @@ tags: [physics, electricity, exponents]
In electronics we are often dealing with units that are very large or very small, thus we rely on [exponents](/Mathematics/Algebra/Exponents.md) for formal expression. In electronics we are often dealing with units that are very large or very small, thus we rely on [exponents](/Mathematics/Algebra/Exponents.md) for formal expression.
| Prefix | Symbol | Expression as exponent | Expression as decimal value | | Prefix | Symbol | Expression as exponent | Expression as decimal value | English word |
| ------ | ------ | ---------------------- | --------------------------- | | ------ | ------ | ---------------------- | --------------------------- | ------------ |
| Giga- | G | $10^9$ | 1,000,000,000 | | Terra- | T | $10^{12}$ | 1,000,000,000,000 | trillion |
| Mega- | M | $10^6$ | 1,000,000 | | Giga- | G | $10^9$ | 1,000,000,000 | billion |
| Kilo- | k | $10^3$ | 1,000 | | Mega- | M | $10^6$ | 1,000,000 | million |
| Milli- | m | $10^{-3}$ | 0.001 | | Kilo- | k | $10^3$ | 1,000 | thousand |
| Micro- | $\mu$ | $10^{-6}$ | 0.0000001 | | Milli- | m | $10^{-3}$ | 0.001 | hundredth |
| Nano- | n | $10^{-9}$ | 0.0000000001 | | Micro- | $\mu$ | $10^{-6}$ | 0.0000001 | thousandth |
| Pico- | p | $10^{-12}$ | 0.0000000000001 | | Nano- | n | $10^{-9}$ | 0.0000000001 | billionth |
| Pico- | p | $10^{-12}$ | 0.0000000000001 | trillionth |
For example, with Amps we tend not to use 1 whole amp as this is far too large for most electronics. More common is the milliampere (mA) and the microampere ($\mu$A). For example, with Amps we tend not to use 1 whole amp as this is far too large for most electronics. More common is the milliampere (mA) and the microampere ($\mu$A).

37
Hardware/Binary/Binary_units_of_measurement.md
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@ -18,23 +18,34 @@ The equivalent entity in the [binary number system](/Hardware/Binary/The_binary_
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. 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 $3^{10} (59049)$: 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:
``` ```
001 00
002 01
003 10
... 11
010
011
012
013
...
``` ```
With the binary number we have $3^{10} (59049)$ ### Bytes
Therefore to express greater complexity we work with sequences of bits.
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. 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. 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.