Question:Why are hard drives never as large as advertised? ?? ??(8 answers) ?? ????Looking for Clarification on Binary Prefix Logic / History vs. SI Prefix ?? ??(1 answer) ?? ???Closed 4 years ago. ?
I was taking a look at a HDD and I found a document (from Toshiba, link: 2.5-Inch SATA HDD mq01abdxxx) that says:
“One Gigabyte (1GB) means 10^9 = 1,000,000,000 bytes using powers of 10. A computer operating system, however, reports storage capacity using powers of 2 for the definition of 1GB = 2 ^30 = 1,073,741,824 bytes, and therefore shows less storage capacity.”
Then powers of 10 are bigger than powers of 2, OK.
Example 10^2 = 100 and 2^2 = 4.
But I do not understand the document which says for the same storage capacity:
1GB is 1,000,000,000 bytes (powers of 10) and 1,073,741,824 bytes (powers of 2), then: it shows less storage capacity (the powers of 2). Why is it less? If I see for 1GB more storage capacity in powers of 2 than powers of 10.
Answer: The historical reason of using powers of 2 is that memory and hard disk are accessed by the CPU using an address space composed of lines on binary code. Hardware producers decided the names in this way:
2^10 = 1024 and as it’s almost 1000 then call it 1 Kilobyte
2^20 = 1048576 bytes and as it’s almost 1000000 then call it 1 Megabyte
For the normal user it is nonsense and cumbersome. In addition the prefixes “kilo”, “mega”, etc. come into conflict with the International System of Units (SI) standard where 1 kiloWatt means 10^3 or 1000 Watts.
To solve the problem, in the year 2000 The International Electrotechnical Commission or IEC proposed a notation scheme for the units based in powers of 2 on the norm ISO/IEC 80000-13.
The new names were created by replacing the second syllable in the old name by bi (referring to 2 ). A kilobyte must be now a kibibyte and so on. The new units also got corresponding symbols, so 10 kibibyte is now written as 10 KiB instead of 10 kB. This is the correspondence table:
Notation ?Symbol ?Value1 kilobyte ?1 kB ?10^3 ?= 1000 bytes1 megabyte ?1 MB ?10^6 ?= 1000000 bytes1 gigabyte ?1 GB ?10^9 ?= 1000000000 bytes1 terabyte ?1 TB ?10^12 = 1000000000000 bytes1 kibibyte ?1 KiB ?2^10 = 1024 bytes1 mebibyte ?1 MiB ?2^20 = 1048576 bytes1 gibibyte ?1 GiB ?2^30 = 1073741824 bytes1 tebibyte ?1 TiB ?2^40 = 1099511627776 bytes
16 years later a lot of hardware and software vendors still refer to the base-2 units with their SI names. A megabyte can mean either 1000000 bytes or 1048576 bytes.
If you buy a 100 GB hard drive, the capacity is 100×10^9 or 10^11 bytes. But, and this is the big but, the operating system will only report the drive as having a capacity of 93 GB (10^11)/(2^30). ?You bought a 100 gigabyte drive, which is equivalent to a 93 gibibyte drive. The operating system is the one that uses the wrong notation.
Drive manufacturers hide this issue with disclaimers and explanations that always lead to the conclusion that actual formatted capacity may be less .