Powerland Computers

We understand that the IT world can be frustrating place with so much information flying around, but we hope to pass on a helpful fact with this article - namely: "There are two systems for measuring memory; binary and decimal." A short time ago, it may have been rightly asked what difference it made. After all, what was the difference between 1024 and 1000 bytes? Indeed, not much (2%).

What, however, is the difference between 750 and 698.5 Gigabytes? 51.5 Gigabytes! 51.5 encyclopedias (1 gigabyte is enough to store approximately one full length encyclopedia complete with graphics, audio, and video). Inquiring minds might want to know where that much memory goes - and hence this article.

In order to understand where our precious storage is going, we must first understand binaries. What is 1+1? To us, it is "2" ("two"); but to a computer, it is "10" ("one-zero") (It has therefore been said, “There are ‘10’ kinds of people in this world – those who understand binary numbers, and those who don’t!”) This is because computers count, and think, in binary or "base-2". We count and think in decimal, or "base-ten". So, what to us is "10" ("ten") is "1010" ("one-zero-one-zero") to a computer.

Below is a table comparing the decimal and binary systems, counting from 1 to decimal "10" ("ten")

Please see Binary/Decimal Converter Calculator

As shown above, in the binary system, "10000000000" ("one-zero-zero..." or "one followed by ten zeros") equals 2¹⁰, or, to us, 1024 ("one thousand, twenty four") - approximately 1000 ("one thousand"). This is how 1024 bytes came to be known as a "kilobyte". As memory sizes grew past "1024 kilobytes", the term "megabytes" came into play. A binary megabyte equals 2²⁰ or 1,048,576 bytes - still not too different from the decimal "1,000,000 bytes"; but the difference becomes 5%, as opposed to 2%. Now that memory sizes have grown past "1024 megabytes", "gigabytes" is the most common term, with the binary to decimal comparison becoming 2³⁰ or 1,073,741,824 bytes to 1,000,000,000 bytes; or 7%. Soon, as far as we can see, the term "terabytes" or "1024 gigabytes" (2⁴⁰ bytes) will take over - where the difference will jump to 9%.

The table below shows such a progression.

Units	Percent Difference	Units of Capacity (decimal)	50	100	250	500	750
KB	2%	Difference	1.2	2.3	5.9	11.7	17.6
KB	2%	Capacity (Binary)	48.8	97.7	244.1	488.3	732.4
MB	5%	Difference	2.3	4.6	11.6	23.2	34.7
MB	5%	Capacity (Binary)	47.7	95.4	238.4	476.8	715.3
GB	7%	Difference	3.4	6.9	17.2	34.3	51.5 (!)
GB	7%	Capacity (Binary)	46.6	93.1	232.8	465.7	698.5

As referred to at the beginning of the article, and illustrated above, there is a 51.5 gigabyte difference between "750" decimal gigabytes and the binary "698.5" equivalent. Again, with "terabytes", the difference is 9%. Therefore, a decimal "terabyte" translates to 0.909 binary "terabytes", leaving a difference of 0.091 terabytes - or 91 gigabytes.

One customer stumbled across this phenomenon when checking his hard drive space in Windows. Windows indicated the hard drive space in binary, reporting a lower capacity than the customer had, literally, bargained for. The difference, we learned, was largely due to the decimal-binary discrepancy explained above. Some might argue that all of this is "too much information", and that customers cannot be bothered to know facts like this.

We, however, thought you might like to know. It has been said that "knowledge is power", and Powerland Computers takes this to heart by publishing this article.

By the way, there is a proposed solution to this confusion. The IEEE (Institute of Electrical and Electronics Engineers), has proposed using different terms for different units of measurement. According to their proposal, a "gigabyte" would always mean "1,000,000,000 bytes, and "Gibibyte" would take over as the term for "2³⁰ = 1,073,741,824 bytes." "Tebibyte" would mean "2⁴⁰ = 1,099,511,627,776 bytes", and - retroactively, "Mebibyte" - "2²⁰ = 1,048,576 bytes" and "Kibibyte" - "2¹⁰ = 1,024 bytes".

Please refer to the table below