From 5d85dc505e24018b89ab1802b40bcbde987cabd3 Mon Sep 17 00:00:00 2001 From: tactonbishop Date: Mon, 3 Oct 2022 11:00:06 +0100 Subject: [PATCH] Last Sync: 2022-10-03 11:00:06 --- ...xes_for_units_of_electrical_measurement.md | 19 +++++----- .../Binary/Binary_units_of_measurement.md | 37 ++++++++++++------- 2 files changed, 34 insertions(+), 22 deletions(-) diff --git a/Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md b/Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md index a0363ca..6c126a8 100644 --- a/Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md +++ b/Electronics/Physics_of_electricity/Prefixes_for_units_of_electrical_measurement.md @@ -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. -| Prefix | Symbol | Expression as exponent | Expression as decimal value | -| ------ | ------ | ---------------------- | --------------------------- | -| Giga- | G | $10^9$ | 1,000,000,000 | -| Mega- | M | $10^6$ | 1,000,000 | -| Kilo- | k | $10^3$ | 1,000 | -| Milli- | m | $10^{-3}$ | 0.001 | -| Micro- | $\mu$ | $10^{-6}$ | 0.0000001 | -| Nano- | n | $10^{-9}$ | 0.0000000001 | -| Pico- | p | $10^{-12}$ | 0.0000000000001 | +| 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 | +| Milli- | m | $10^{-3}$ | 0.001 | hundredth | +| Micro- | $\mu$ | $10^{-6}$ | 0.0000001 | thousandth | +| 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). diff --git a/Hardware/Binary/Binary_units_of_measurement.md b/Hardware/Binary/Binary_units_of_measurement.md index 1d34030..ba62562 100644 --- a/Hardware/Binary/Binary_units_of_measurement.md +++ b/Hardware/Binary/Binary_units_of_measurement.md @@ -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. -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 -002 -003 -... -010 -011 -012 -013 -... +00 +01 +10 +11 ``` -With the binary number we have $3^{10} (59049)$ -Therefore to express greater complexity we work with sequences of bits. +### 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. -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.