An order of magnitude is generally a factor of ten. A quantity growing by four orders of magnitude implies it has grown by a factor of 10000 or 104. However, because computers are binary, orders of magnitude are sometimes given as powers of two.
This article presents a list of multiples, sorted by orders of magnitude, for bit rates measured in bits per second. Since some bit rates may measured in other quantities of data or time (like MB/s), information to assist with converting to and from these formats is provided. This article assumes the following:
- A group of 8 bits (8 bit) constitutes one byte (1 B). The byte is the most common unit of measurement of information (megabyte, mebibyte, gigabyte, gibibyte, etc.).
- The decimal SI prefixes kilo, mega etc., are powers of 10. The power of two equivalents are the binary prefixes kibi, mebi, etc.
Accordingly:
- 1 kB (kilobyte) = 1000 bytes = 8000 bits
- 1 KiB (kibibyte) = 210 bytes = 1024 bytes = 8192 bits
- 1 kbit (kilobit) = 125 bytes = 1000 bits
- 1 Kibit (kibibit) = 210 bits = 1024 bits = 128 bytes
| Factor (bit/s) | SI prefix | Value | Field | Item |
|---|---|---|---|---|
| 10−2 | 5.0×10−2 bit/s | Text data | Project ELF bit rate for transmitting 3-letter codes to US nuclear submarines [1][2] | |
| 100 | bit/s | |||
| 101 | 5.0×101 bit/s | Positioning system | Bit rate for transmissions from GPS satellites [3] | |
| 5.6×101 bit/s | Text data | Bit rate for a skilled operator in Morse code[4] | ||
| 103 | kbit/s | 4×103 bit/s | Audio data | Minimum achieved for encoding recognizable speech (using special-purpose speech codecs) |
| 8×103 bit/s | Audio data | Low bit rate telephone quality | ||
| 104 | ||||
| 3.2×104 bit/s | Audio data | MW quality and ADPCM voice in telephony, doubling the capacity of a 30 chan link to 60 ch. | ||
| 5.6×104 bit/s | Networking | 56kbit modem – 56 kbit/s – 56,000 bit/s | ||
| 6.4×104 bit/s | Networking | 64 kbit/s in an ISDN B channel or best quality, uncompressed telephone line. | ||
| 105 | 1.28×105 bit/s | Audio data | 128 kbit/s MP3 – 128,000 bit/s | |
| 1.92×105 bit/s | Audio data | Nearly CD quality[citation needed] for a file compressed in the MP3 format | ||
| 106 | Mbit/s | 1.4112×106 bit/s | Audio data | CD audio (uncompressed, 16 bit samples × 44.1 kHz × 2 channels) |
| 1.536×106 bit/s | Networking | 24 channels of telephone in the US, or a good VTC T1. | ||
| 2×106 bit/s | Video data | 30 channels of telephone audio or a Video Tele-Conference at VHS quality | ||
| 8×106 bit/s | Video data | DVD quality | ||
| 107 | 1×107 bit/s | Networking | Classic Ethernet | |
| 1×107 bit/s | Biology | Research suggests that the human retina transmits data to the brain at the rate of ca. 107 bit/sec[5][6] | ||
| 2.7×107 bit/s | Video data | HDTV quality | ||
| 108 | 1×108 bit/s | Networking | Fast Ethernet | |
| 4.8×108 bit/s | Computer data interfaces | USB 2.0 High-Speed (interface signalling rate) | ||
| 7.86×108 bit/s | Computer data interfaces | FireWire IEEE 1394b-2002 S800 | ||
| 9.5×108 bit/s | Computer storage | Harddrive read, Samsung SpinPoint F1 HD103Uj [7] | ||
| 109 | Gbit/s | 1×109 bit/s | Networking | Gigabit Ethernet |
| 1.067×109 bit/s | Computer data interfaces | Parallel ATA UDMA 6; conventional PCI 32 bit 33 MHz – 133 MB/s | ||
| 1.244×109 bit/s | Networking | OC-24, a 1.244 Gbit/s SONET data channel | ||
| 1.5×109 bit/s | Computer data interfaces | SATA 1.5 Gbit/s – First generation (interface signaling rate) | ||
| 3×109 bit/s | Computer data interfaces | SATA 3Gbit/s – Second generation (interface signaling rate) | ||
| 5×109 bit/s | Computer data interfaces | USB 3.0 SuperSpeed (interface signaling rate) | ||
| 6×109 bit/s | Computer data interfaces | SATA 6Gbit/s – Third generation (interface signaling rate) | ||
| 8.533×109 bit/s | Computer data interfaces | PCI-X 64 bit 133 MHz – 1,067 MB/s | ||
| 9.953×109 bit/s | Networking | OC-192, a 9.953 Gbit/s SONET data channel | ||
| 1010 | 1.0×1010 bit/s | Computer data interfaces | Thunderbolt | |
| 1.0×1010 bit/s | Networking | 10 Gigabit Ethernet | ||
| 1.0×1010 bit/s | Computer data interfaces | USB 3.1 SuperSpeed 10 Gbit/s (interface signaling rate) | ||
| 3.9813×1010 bit/s | Networking | OC-768, a 39.813 Gbit/s SONET data channel, the fastest in current use | ||
| 4.0×1010 bit/s | Networking | 40 Gigabit Ethernet | ||
| 8×1010 bit/s | Computer data interfaces | PCI Express 2.0 ×16 (interface signaling rate) | ||
| 9.6×1010 bit/s | Computer data interfaces | InfiniBand 12X QDR | ||
| 1011 | 1.0×1011 bit/s | Networking | 100 Gigabit Ethernet | |
| 1.28×1011 bit/s | Computer data interfaces | PCI Express 3.0 ×16 (interface signaling rate) | ||
| 2.0×1011 bit/s | Networking | 200 Gigabit Ethernet | ||
| 2.56×1011 bit/s | Computer data interfaces | PCI Express 4.0 ×16 (interface signaling rate) | ||
| 4.0×1011 bit/s | Networking | 400 Gigabit Ethernet | ||
| 5.12×1011 bit/s | Computer data interfaces | PCI Express 5.0 ×16 (interface signaling rate) | ||
| 1012 | Tbit/s | 1.28×1012 bit/s | Networking | SEA-ME-WE 4 submarine communications cable – 1.28 terabits per second [8] |
| 3.84×1012 bit/s | Networking | I-ME-WE submarine communications cable – design capacity of 3.84 terabits per second [9] | ||
| 1014 | 2.45×1014 bit/s | Networking | Projected average global internet traffic in 2015 according to Cisco's 2011 VNI IP traffic forecast [10][11] | |
| 1015 | Pbit/s | 1.050×1015 bit/s | Networking | Data rate over a 14 transmission core optical fiber developed by NEC and Corning researchers.[12] |
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Orders of magnitude exercise example 2 | Pre-Algebra | Khan Academy
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Big O Notations
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Unit Conversion & Significant Figures: Crash Course Chemistry #2
Transcription
Let's do a few more examples from the orders of magnitude exercise. Earth is approximately 1 times 10 to the seventh meters in diameter. Which of the following could be Earth's diameter? So this is just an approximation. It's an estimate. And they're saying, which of these, if I wanted to estimate it, would be close or would be 1 times 10 to the seventh? And the key here is to realize that 1 times 10 to the seventh is the same thing as one followed by seven zeroes. One, two, three, four, five, six, seven. Let me put some commas here so we make it a little bit more readable. Or another way of talking about it is that it is, 1 times 10 to the seventh, is the same thing as 10 million. So which of these, if we were to really roughly estimate, we would go to 10 million. Well, this right over here is 1.271 million, or 1,271,543. If I were to really roughly estimate it, I might go to one million, but I'm not going to go to 10 million. So I'd rule that out. This is 12,715,430. If I were to roughly estimate this, well, yeah. I would go to 10 million. 10 million is if I wanted really just one digit to represent it, if I were write this in scientific notation. This right over here is 1.271543 times 10 to the seventh. Let me write that down. 12,715,430. If I were to write this in scientific notation as 1.271543 times 10 to the seventh. And when you write it this way, you say, hey, well, yeah, if I was to really estimate this and get pretty rough with it, and I just rounded this down, I would make this 1 times 10 to the seventh. So this really does look like our best choice. Now let me just verify. Well, this right over here, if I were to write it, I would go to 100 million, or 1 times 10 to the eighth. That's way too big. And this, if I were to write it, I would go to a billion, or 1 times 10 to the ninth. So that's also too big. So once again, this feels like the best answer. Now let's try a couple more. So here we're asked, how many times larger is 7 times 10 to the fifth than 1 times 10 to the fourth? Well, we could just divide to think about that. So 7 times 10 to the fifth divided by 1 times 10 to the fourth. Well, this is the same thing as 7 over 1 times 10 to the fifth over 10 to the fourth, which is just going to be equal to-- well, 7 divided by 1 is 7. And 10 to the fifth, that's multiplying five 10's. And then you're dividing by four 10's. You're going to have one 10 left over. Or, if you remember your exponent properties, this would be the same thing as 10 to the 5 minus 4 power, or 10 to the first power. So this right over here, all of this business, is going to simplify to 10 to the first, or I could actually write it this way. This would be the same thing as 10 to the 5 minus 4, which is equal to 10 to the 1, which is just equal to 10. So this is 7 times 10, which is equal to 70. So 7 times 10 to the fifth is 70 times larger than 1 times 10 to the fourth. Let's do one more. So here, they're asking us 3 times 10 to the ninth is 30,000 times larger than what number? So once again, we can divide. So we have 3 times 10 to the ninth is 30,000 times larger than what number? So let's just divide by 30,000 and see what we get. And here we've written something in kind of an exponential notation, or we should say scientific notation actually. And here, we just wrote the number out. So one way we could do it is we could either write this number out and then divide, or we could write this in scientific notation. So let's do it either way. So if we were to expand the top number out, we could write that as 3 followed by nine zeros. One, two, three, four, five, six, seven, eight, nine. Let me put some commas here to make it readable. And then we're dividing that by 3 followed by four zeros. One, two, three, four. And then we could cancel out the zeros. We could say, OK, let's divide the top and the bottom by 10. Let's divide it by another 10, by another 10, by another 10. And then, let's see, we've done all the dividing by 10. And now let's divide the top and the bottom by 3. So this would become a 1. This would become a 1. So on the bottom, we're just left with a 1. And we'd have 1 followed by one, two, three, four, five zeros. So this would be 1 followed by one, two, three, four, five zeros, or 100,000. Now let's write it, both of these, in scientific notation. So 3 times 10 to the ninth, I'm just going to rewrite that as 3 times 10 to the ninth. And we're dividing that by 30,000, which is the exact same thing as 3 times 10 to the-- we have one, two, three, four zeros here. 3 times 10 to the fourth. Or I guess I really should say, we have four places after the three. So one, two, three, four. So 3 times 10 to the fourth. And so we could divide the 3 by the 3, and then that will simplify. So 3 divided by 3 is just 1. And then 10 to the ninth divided by 10 to the fourth, well that's going to be 10 to the 9 minus 4, 10 to the fifth. So it's going to be 1 times 10 to the fifth, which, once again, is 1 followed by five zeros, or the exact same thing as 100,000. So it's 30,000 times larger than 100,000.
See also
- Data-rate units
- List of interface bit rates
- Spectral efficiency
- Orders of magnitude (data)
- Orders of magnitude (time)
References
- ^ Heppenheimer, T. A. (April 1987). "Signaling Subs". Popular Science. 230 (4). New York: 44–48.
- ^ Source specifies a transmission rate of 3 characters in 5 minutes. An uppercase character can be represented with 5 bits.
- ^ "The Promising Marriage of Wireless and GPS Technologies" (PDF). U-blox. November 2009. p. 7. Retrieved 5 August 2013.
- ^ WPM, or Words Per Minute, is the number of times the word "PARIS" is transferred per minute. Strictly speaking the code is quinary, accounting inter-element, inter-letter, and inter-word gaps, yielding 50 binary elements (bits) per one word. Therefore 40 wpm is 2000 bits/min or 55.6 bit/s. Counting characters, including inter-word gaps, gives six characters per word or 240 characters per minute, and finally four characters per second.
- ^ Penn researchers calculate how much the eye tells the brain, 26 July 2006
- ^ How Much the Eye Tells the Brain
- ^ "Samsung overtakes".
- ^ "Fujitsu Completes Construction of SEA-ME-WE 4 Submarine Cable Network". Fujitsu Press Releases. Fujitsu. 13 December 2005. Archived from the original on 17 March 2007. Retrieved 31 January 2008.
- ^ "Imewe Picks Alcatel-Lucent". LR Mobile News. 11 February 2008. Archived from the original on 23 May 2016. Retrieved 4 August 2013.
- ^ "Cisco: The Internet Is, Like, Really Big, and Getting Bigger". Dow Jones & Company. 1 June 2011. Retrieved 5 August 2013.
- ^ Calculated based on Cisco's figure of 966 exabytes per year, using the astronomical definition of a Julian year (365.25 days per year, 86,400 seconds per day).
- ^ "NEC, Corning claim petabit transmission over a single optical fiber". PennWell. 17 January 2013. Retrieved 4 August 2013.
This page was last edited on 21 May 2024, at 01:45