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KiloBytes vs. kilobits vs. Kibibytes: Supplements

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Author: lyberty
Article last updated: October 13, 2005

[ tech/computing ]
[ ]

Main article: K = 1,024; k= 1,000 ; B = Bytes ; b= bits

On this page: DVD Read Speeds

Okay, here's the problem.

If you're talking about data transfer rates for Hard Disk Drives,
you need to use BITS in your discussion. This is because you are measuring PULSES (hertz and bits). [A megabit is a million binary pulses, or 1,000,000 (that is, 10^6) pulses (or "bits").Although the bit is a unit of the binary number system, bits in data communications are discrete signal pulses and have historically been counted using the decimal number system.]

But if you need to switch to Bytes for some reason, you are now talking about File Transfer speeds, which is a measurement of how fast you can move BYTES (not bits). For example, "how long will it take to transfer this file that is 200 MB?" Now you are in the world of base-2 (/1,024), because your computer is using the binary number system for Storage. So now you're asking (using the previous example) "How long to transfer 209,715,200 bytes?"

Note that SATA-IO refers to BIT-RATES for precisely this reason (1.5Gb/s and 3.0Gb/s).

In summary:
Discussion of data transfer rates are in bits, even if you are talking about file transfer speeds.
If you need to refer to Bytes for some reason, you must switch to base-2 (/1,024),

Therefore:
1.5 Gbps* = 187,500,000 Bytes per second = (approx) 178.81 MB/s.
and
3.0 Gbps* = ((3*1,000,000,000) /8) /1,048,576 = (approx) 357.63 MB/s.

You may not "give a damn", but it affects your answer.

So a different answer would be:

[quote]These are the correct ones:
1.5 Gb/s = 179 MB/s
3.0 Gb/s = 358 MB/s
[/quote]

See what I mean?


References:
[url]http://searchstorage.techtarget.com/sDefinition/0,,sid5_gci212534,00.html[/url]

[url]http://www.lyberty.com/encyc/articles/kb_kilobytes.html[/url]

[posted to]


Another example (DSL/ADSL) :

Upload Speed (as reported in Azureus): [ 36.5kB/s ]
U: (36.5KB*1024) = B/s ; B/s*8= bps ; bps/1000= kbps
U: (37,376 BYTES-per-second) --*8--> 299,008 bps --/1000--> 299.008 kbps 299 kbps (thousand-bits-per-second) upload speed


PCI Bus Speed: 32-bit @ 33 Mhz

The PCI bus with the usual 32 bit and 33 MHz has a theoretical maximum of about 1,056,000,000 bits per second (bps)

132 MB/s = 132 000 000 Bytes = 1 056 000 000 bits or 1056 mbps or 1.056 gbps.
((if b1024: 132 000 000 Bytes = 125.88501 MegaBytes))

keywords: transfer 32 bit and 33 MHz Gb/s, 32 bit 33 Mhz PCI Gbps, bit rate PCI 33-MHz

The PCI bus with the usual 32 bit and 33 MHz (2002) is capable of (in theory) up to (sometimes referred to as 132 MB/s);
in practice, however, this suffers due to the fact that the bus is used equally by all the connected devices.

"The original 33-MHz, 32-bit implementation [of PCI] delivers a peak theoretical bandwidth of 133 million bytes per second (MB/sec)."

You need to keep in mind the (theor.) peak of the PCI bus :
* 32 bits/33 Mhz : aggregated ideal peak at 132 MB/s
* 64 bits/33 Mhz : aggregated ideal peak at 264 MB/s
* 64 bits/66 Mhz : aggregated ideal peak at 528 MB/s

 

---

July 25, 2005 - "EMC shares slipped by 24 cents to $14.25 after the data-storage technology company unveiled the newest version of its high-end, Symmetrix storage system. EMC said the system can store more than a quadrillion bytes of data, or the equivalent of 250 million digital songs."


DVD Read Speeds:
4x 5,568 to 5,632 KB/s
4.5x 6,272 to 6,336 KB/s
5x 6,912 to 6,976 KB/s
5.5x 7,616 to 7,680 KB/s
6x 8,320 to 8,384 KB/s
6.5 9,024 to 9,088 KB/s

bits and bytes: 1 Byte = 8 bits; kbps* 0.1220703125 = KB/s

Internet Speed

File Download Speed

256 kbps

~31.3 KB/s

384 kbps

~46.9 KB/s

512 kbps

~62.5 KB/s

768 kbps

~93.8 KB/s

1 mbps

~122.1 KB/s

kbps = kilobits per second
mbps = megabits per second
KB/s = KiloBytes per second
To convert from network speed (kilobits per second, kbps) to transfer rates (KiloBytes per second, KB/s), multiply by 0.1220703125.

To get bit rate (speed) from values given in Bytes, you must devide the total number of Bytes by 8. To get KB/s values from bit rates, you must multiply the total number of bits by 8, then divide by 1,024.

For converting KB/s to kbps, therefore, the equation is basically as follows:

<K> KiloBytes * 1,024 = <t> total Bytes
<t> total Bytes * 8 = <b> bits
<b> bits / 1,000 = <k> kilobits

And for kbps to KB/s, you switch the equations: <k> kilobits per second * 1,000= <b> total bits per second; <b> bits / 8 = <t> total Bytes per second; and <t> / 1,024 = <K> KiloBytes per second.
For example: 128 kbps (k) = 128,000 bits per second (k*1000=b) = 16,000 bytes per second (b/8=t) , or about 15.6 KB/s (t/1,024=K) .

So a 512\128 internet connection would give you about 62.5 KB/s maximum download, and about 15.6 KB/s upload (max).
And a 1500\128 service (1.5 mbps down) would give you about 183.1 KiloBytes per second, maxium. [5]
[convert 128 kbps to KB/s : ((128*1000)/8)/1024 ; ratio 128x=15.625; x= 0.1220703125]
[convert 256 kbps to KB/s: ((256*1000)/8)/1024= 31.25 ; 256x=31.25; x=0.1220703125]
[convert 512 kbps to KB/s : ((512*1000)/8)/1024; ratio 512x=62.500; x= 0.1220703125]
[convert 1 mbps to KB/s : ((1000*1000)/8)/1024=122.070312; ratio 1000x=122.0703125; divide by 1000 and x=0.1220703125]


	512 kbps = 512,000 bits-per-second; 512,000/8 = 64,000 Bytes per second; 64,000/1,024 = 62.5 KiloBytes; in other words, 62.5 KB/s. 
	 Google calculator shows "512 kbps = 64 kilobytes / second"; they mean 64000 bytes per second.
	 128 kbps = 128,000 bits-per-second; 128,000/8 = 16,000 Bytes per second; 16,000/1,024 = 15.625 KiloBytes; in other words, about 15.6 KB/s.


 

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Sample usage.

From: http://compnetworking.about.com/cs/wireless/f/wirelessspeed.htm
Author: Bradley Mitchell
Date: unknown

-- start quote --

The speed of a wireless network depends on several factors.

First, wireless local area networks (W-LANs) feature differing levels of performance depending on which Wi-Fi standard they support.

802.11b W-LANs offer maximum theoretical bandwidth of 11 [mbps>.
802.11a and 802.11g W-LANs offer theoretical bandwidth up to 54 [mbps]. (In contrast, typical wired Ethernets run at 100 [mbps].)

The performance of Wi-Fi networks in practice never approaches the theoretical maximum.
802.11b networks, for example, generally operate no faster than about 50% of theoretical peak, or 5.5 [mbps>.
Likewise, 802.11a and 802.11g networks generally run no faster than 20 [mbps]. The disparity between theoretical and practical performance comes from protocol overhead, signal interference, and decreasing signal distance with distance. In addition, the more devices communicating on a WLAN simultaneously, the slower the network will appear.

On home networks, keep in mind that the performance of an Internet connection is often the limiting factor in network speed. Even though files can be shared on a wireless LAN at speeds of 5 or 20 Mbps, wireless clients will still connect to the Internet at the speed typically offered by Internet Service Providers, usually less than 1 [mbps] (1000 kbps). [*2]

Finally, wireless network technology is capable of more speed than what Wi-Fi supports today. Industry vendors continue to develop improved technologies like 802.16 WiMAX that offer wireless communications with faster speeds and longer range.

-- end quote --


[*1]
What happened to the other 27.5 GB?

A typical "120GB" Hard Drive under Windows XP:


...so a 120BB Hard Drive (HDD) is actually 111.759 GB.

[HINT: Use Start > Run > "diskmgmt.msc" to check your own disk(s).]

(About Extended Industry Standard Architecture (EISA) partion, also known as 'the Utility Partition':
In Disk Management, an OEM partition typically is displayed as an EISA configuration partition.)

EISA Configuration Partition (also known as the Utility Partition), you can blow that away if you don't need it. If it won't delete from Disk Management, use the SCSI Configuration Utility to do a low-level format of the drive; that will get rid of it.



  ----


[*2] As an example, a typical "broadband" (aka "HighSpeed") service for asynchronous DSL (as of August 2005) would be "1.5\384", meaning 1.5 mbps upload\384 kbps download;
this would typically give you about a 1200 kbps maximum download speed, and about a 318 kbps maximum upload speed.

If you are maxing out at about 30 KB/s (KiloBytes) per second upload, you are uploading data at a rate of around 245 or 246 kbps.
[((246 * 1,000) / 8) / 1,024 = 30.0292969. Also, 30*Y=245.76; Y=8.192]


[3] Common misspellings; petrabyte, tetrabyte, petrayte; bianary, ... Other keywords: Calculate bandwidth throughput for any device - convert from Kbps and MB/s to
... 1 Kbps, 1 Mbps, 1 Gbps, 1 Tbps. 512K ADSL modem [Broadband]. 512 Kbps ...


[4] From "whatis.techtarget.com":


megabit
- In data communications, a megabit is a million binary pulses, or 1,000,000 (that is, 10^6) pulses (or "bits").
It's commonly used for measuring the amount of data that is transferred in a second between two telecommunication points. For example, a U.S. phone company T-carrier system line is said to "sustain a data rate of 1.544 megabits per second." Megabits per second is usually shortened to mbps.

Some sources define a megabit to mean 1,048,576 (that is, 2^20) bits. Although the bit is a unit of the binary number system, bits in data communications are discrete signal pulses and have historically been counted using the decimal number system. For example, 28.8 kilobits per second (Kbps) is 28,800 bits per second. Because of computer architecture and memory address boundaries, bytes are always some multiple or exponent of two. See kilobyte, etc.

GigaByte - A gigabyte (pronounced GIG-ah-bite with hard G's) is a measure of computer data storage capacity, equal to approximately a billion bytes. Specifically, a gigabyte is two to the 30th power [2^30] bytes, or 1,073,741,824 (one billion, seventy three million, seven hundred fourty one thousand, eight hundred twenty four) bytes in decimal notation.


[5] "These are optimum bandwidths. Actual bandwidth may vary due to network traffic and and are not guaranteed. The difference between maximum speed and average speed can be especially large in wireless technology, or cable internet. The varying amount of data traffic on the Internet (and your own LAN, if applicable) and the condition of your computer equipment affect the speed of any connection at any given time." ; "Keep in mind that [even with a 1.5 mbps connection] you will not normally see 1.5 megabits in a speed test ... due to overhead the more commonly seen speed with this type of connection is in the neighborhood of 1200-1250."
See: broadbandreports.com


[6] Further historical reference for "kibi-" nomenclature:
* NIST "Tech Beat"; "Get Ready for the mebi, gibi and tebi"  (March 1999)
* http://www.worldwidewords.org/turnsofphrase/tp-kib1.htm  (August 1999)

[7] (from Tom's Hardware Community:)

Nearly everyone (including the experts) gets this wrong but the theoretical limit of a PCI bus is 127.2 MB/s, not 133 MB/s .

The bus is 32 bits wide and clocked at 33.3 Mhz. So many people assume its 32/8*33.3. But this ignores the fact that the "M" in Mhz = 1,000,000, while the "M" in MB = 1,048,576.

(bytes)*(MEGAHertz) = total throughput, in bytes, per second <T>
<T> / 1,024 = total throughput, in KiloBytes, per second.
<T> / 1,048,576 = total throughput, in MegaBytes, per second.

( (32/8)*(33.3*1,000,000) )/1,048,576= 127.2 MB/s

1 /1,024 /1,024 = 0.00000095367431640625
1 /1,048,576 = 0.00000095367431640625

 

  


 
Links:

"Binary vs. Decimal Measurements" {pcguide.com}

whatis.com -- Table of Physical Units {whatis.techtarget.com}

Capacities of DVD (the DVD faq) {dvddemystified.com/dvdfaq}
  ("[7.2] Notation and units")

The National Institute of Standards and Technology - "SI Prefixes for binary multiples"

How Many Bytes for Anything (How many Bytes for...) {techtarget.com}
[e.g. "10 terabytes for the print collections of the U.S. Library of Congress"]

About Bits n' Bytes and Speed (DSLReports.com; the AOL FAQ) [2002-2004]


SATA/300 or SATA-II


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