Back Of The Envelope Estimation & Powers of Two
Data Volume Units Using the (Power of two)
A byte is a sequence of 8 bits. An ASCII character uses one byte of memory (8 bits). Below is a table explaining the data volume unit.
Powers of two are often used to measure computer memory. A byte is now considered eight bits (an octet), resulting in the possibility of 256 values (2<sup>8). (The term byte once meant (and in some cases, still means) a collection of bits, typically of 5 to 32 bits, rather than only an 8-bit unit.))
| Power | Approx. Value | Exp | Short Name | # of Zeros |
|---|---|---|---|---|
| 10 | 1 Thousand | 2<sup>10 | 1 KB | 1_024 |
| 20 | 1 Million | 2<sup>20 | 1 MB | 1_048_576 |
| 30 | 1 Billion | 2<sup>30 | 1 GB | 1_073_741_824 |
| 40 | 1 Trillion | 2<sup>40 | 1 TB | 1_099_511_627_776 |
| 50 | 1 Quadrillion | 2<sup>50 | 1 PB | 1_125_899_906_842_624 |
# 1KB
# 1_024
iex > :math.pow(2, 10) |> round
# 1MB
# 1_048_576
iex > :math.pow(2, 20) |> round
# 1GB
# 1_073_741_824
iex > :math.pow(2, 30) |> round
# 1TB
# 1_099_511_627_776
iex > :math.pow(2, 40) |> round
# 1PB
# 1_125_899_906_842_624
iex > :math.pow(2, 50) |> roundLatency
ms = millisecond, µs = microsecond, ns = nanosecond
1 ms = 10^-3 seconds = 1,000 µs = 1,000,000 ns
1 µs = 10^-6 seconds = 1,000 ns
Interesting Inverse Comparisons
| In Seconds | Name | S Exp | v | Short Name | PwrOf2 | Exp Approx
|————-|————|———-|—|————-|———|——
|1 ms | millisecond| 10^-3 | | ~1 KB |2<sup>10 | ~10^3
|1 µs | microsecond| 10^-6 | | ~1 MB |2<sup>20 | ~10^6
|1 ns | nanosecond | 10^-9 | | ~1 GB |2<sup>30 | ~10^9
