| Bits per second (bit/s) | Exbioctets per second (Eio/s) |
|---|---|
| 1 Bit per second | 1.08420217249 × 10-19 Eio/s |
| 2 Bits per second | 2.16840434497 × 10-19 Eio/s |
| 3 Bits per second | 3.25260651746 × 10-19 Eio/s |
| 4 Bits per second | 4.33680868994 × 10-19 Eio/s |
| 5 Bits per second | 5.42101086243 × 10-19 Eio/s |
| 10 Bits per second | 1.08420217249 × 10-18 Eio/s |
| 20 Bits per second | 2.16840434497 × 10-18 Eio/s |
| 25 Bits per second | 2.71050543121 × 10-18 Eio/s |
| 50 Bits per second | 5.42101086243 × 10-18 Eio/s |
| 100 Bits per second | 1.08420217249 × 10-17 Eio/s |
| Reference | Bits per second (bit/s) | Exbioctets per second (Eio/s) |
|---|---|---|
| A dial-up modem | 56000 bit/s | 6.07153 × 10-15 Eio/s |
| Typical home broadband | 100000000 bit/s | 1.0842 × 10-11 Eio/s |
| Gigabit Ethernet | 1 × 109 bit/s | 1.0842 × 10-10 Eio/s |
| Streaming a 4K film | 25000000 bit/s | 2.71051 × 10-12 Eio/s |
The bit per second is the fundamental unit of data transfer rate. Its symbol is bit/s, often written bps. It counts how many binary decisions a channel carries in one second, and every other unit of transmission speed is a multiple of it.
Because it is a rate, it has the form of a quantity divided by time, exactly like metres per second or litres per second. That makes the arithmetic straightforward: a link running at a given number of bits per second, multiplied by a duration in seconds, gives the total number of bits transferred, and dividing by eight converts that to octets.
The unit must be distinguished from the baud, which counts symbols per second rather than bits. Early modems transmitted one bit per symbol, so the two numbers were the same and the words were used interchangeably. Modern schemes encode several bits in each symbol — by varying phase and amplitude together — so a channel running at 3,000 baud may carry 33,600 bits per second. Only the bit rate describes how much information moves.
Claude Shannon established the theoretical ceiling in 1948. The capacity of a channel in bits per second depends on its bandwidth and on the ratio of signal to noise, and no coding scheme can exceed it. Every advance in modem and radio design since has been an attempt to approach that limit more closely, and modern systems come within a fraction of a decibel of it.
In practice the raw bit rate of a link is never the rate at which useful data arrives. Protocol headers, error-correcting codes, acknowledgements and retransmissions all consume capacity, and the usable fraction is typically 90 to 95 per cent on a wired link and considerably less on a shared wireless one.
Single bits per second are rarely quoted, because almost every channel is faster. The exceptions are deep-space communication, where a probe billions of kilometres away may return data at a few tens of bits per second, and certain low-power sensor networks that transmit a handful of bits at long intervals to preserve battery life.
One bit per second equals 0.125 octets per second, 0.001 kilobits per second, or about 0.0009766 kibibits per second.
The exbioctet per second is a unit of data transfer rate equal to 1,024 pebioctets per second, or two to the sixtieth power octets per second. Its symbol is Eio/s. It is the binary counterpart of the exaoctet per second, and the two differ by 15.3 per cent.
No machine, network or aggregate reaches this rate. An exbioctet per second is more than eight times the total instantaneous traffic of the entire internet, and it would move the world's whole stock of stored data in a matter of minutes. The unit describes a capacity with no source that could supply it and no destination that could take it in.
Two to the sixtieth is nevertheless a familiar number in computing, because it is the size of the address space a 64-bit machine can reach in octets divided by sixteen. The same power of two turns up in filesystem limits, in memory maps and in the design of every system built on that architecture, so the quantity is well known even though no rate approaches it.
The unit exists because the IEC series was defined completely. Every binary prefix pairs with every unit, exactly as every metric prefix does, so that a reader who has never seen Eio/s can decode it from the prefix alone. A system with gaps would need a table of permitted combinations, which is precisely what a rule-based system exists to avoid.
The difference from the decimal unit is worth restating at each level because it compounds. At the kibioctet it was 2.4 per cent, here it is more than an eighth, and at the yobioctet it will be more than a fifth. That growth is the reason the binary prefixes were created, and it is why the lowercase i has to be written even in figures nobody will check.
For a converter, the treatment is mechanical: six multiplications by 1,024 from octets, or the equivalent divisions coming down. The value of doing it correctly is not that anyone will use the result, but that a tool which handles every case the same way can be trusted on the cases that matter.
One exbioctet per second equals 1,024 pebioctets per second, 1,152,921,504,606,846,976 octets per second, or about 1.153 exaoctets per second.