Why is hex a useful system

Even though English has names for several non-decimal powers pair for the first binary power, score for the first vigesimal power, dozen , gross , and great gross for the first three duodecimal powers , no English name describes the hexadecimal powers decimal 16, , , , Some people read hexadecimal numbers digit by digit like a phone number: 4DA is "four-dee-ay".

However, the letter A sounds like "eight", C sounds like "three", and D can easily be mistaken for the "-ty" suffix: Is it 4D or forty? Systems of counting on digits have been devised for both binary and hexadecimal. Arthur C. Another system for counting up to FF 16 10 is illustrated on the right; it seems to be an extension of an existing system for counting in twelves dozens and grosses , that is common in South Asia and elsewhere.

However, some [ who? Just as decimal numbers can be represented in exponential notation so too can hexadecimal. By convention, the letter p represents times two raised to the power of , whereas e serves a similar purpose in decimal. The number after the p is decimal and represents the binary exponent. Usually the number is normalised: that is, the leading hexadecimal digit is 1 unless the value is exactly 0.

Example: 1. Hexadecimal exponential notation is required by the IEEE binary floating-point standard. Most computers manipulate binary data, but it is difficult for humans to work with the large number of digits for even a relatively small binary number.

Although most humans are familiar with the base 10 system, it is much easier to map binary to hexadecimal than to decimal because each hexadecimal digit maps to a whole number of bits 4 This example converts 2 to base ten.

Since each position in a binary numeral can contain either a 1 or a 0, its value may be easily determined by its position from the right:. With little practice, mapping 2 to F 16 in one step becomes easy: see table in Written representation. The advantage of using hexadecimal rather than decimal increases rapidly with the size of the number.

When the number becomes large, conversion to decimal is very tedious. However, when mapping to hexadecimal, it is trivial to regard the binary string as 4-digit groups and map each to a single hexadecimal digit.

This example shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results. Compare this to the conversion to hexadecimal, where each group of four digits can be considered independently, and converted directly:. The octal system can also be useful as a tool for people who need to deal directly with binary computer data. Octal represents data as three bits per character, rather than four. As with all bases there is a simple algorithm for converting a representation of a number to hexadecimal by doing integer division and remainder operations in the source base.

In theory, this is possible from any base, but for most humans only decimal and for most computers only binary which can be converted by far more efficient methods can be easily handled with this method. The following is a JavaScript implementation of the above algorithm for converting any number to a hexadecimal in String representation. Its purpose is to illustrate the above algorithm. To work with data seriously, however, it is much more advisable to work with bitwise operators.

It is also possible to make the conversion by assigning each place in the source base the hexadecimal representation of its place value and then performing multiplication and addition to get the final representation. That is, to convert the number B3AD to decimal one can split the hexadecimal number into its digits: B 11 10 , 3 3 10 , A 10 10 and D 13 10 , and then get the final result by multiplying each decimal representation by 16 p , where p is the corresponding hex digit position, counting from right to left, beginning with 0.

Most modern computer systems with graphical user interfaces provide a built-in calculator utility, capable of performing conversions between various radices, in general including hexadecimal. In Microsoft Windows , the Calculator utility can be set to Scientific mode called Programmer mode in some versions , which allows conversions between radix 16 hexadecimal , 10 decimal , 8 octal and 2 binary , the bases most commonly used by programmers. In Scientific Mode, the on-screen numeric keypad includes the hexadecimal digits A through F, which are active when "Hex" is selected.

In hex mode, however, the Windows Calculator supports only integers. As with other numeral systems, the hexadecimal system can be used to represent rational numbers , although recurring digits are common since sixteen 10h has only a single prime factor two :.

For any base, 0. One example would be adding a hex and binary value together, and then viewing the result in decimal format. It also supports octal. It will subtract, divide, add, and multiply any two hex values you give it, and instantly show all the answers on the same page. It also shows the decimal equivalents next to the hex answers. The word hexadecimal is a combination of hexa meaning 6 and decimal Binary is base-2, octal is base-8, and decimal is, of course, base Hexadecimal values are sometimes written with the prefix 0x 0x2F7 or with a subscript 2F7 16 , but it doesn't change the value.

In both of these examples, you could keep or drop the prefix or subscript and the decimal value would remain Hexadecimal code is technically a low-level programming language since programmers use it to translate binary code. The processor can't actually understand hexadecimal code.

It's just a shorthand for programmers. Swedish American engineer John Williams Nystrom developed the hexadecimal notation system in Also known as the tonal system, Nystrom's original proposal had applications in various fields, including mathematics and metrology.

If you use the Steam gaming service , your Steam hex is the same as your Steam ID, which is represented in hexadecimal. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads.

Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products.

List of Partners vendors. Tim Fisher. VP and General Manager, Lifewire. Facebook Twitter LinkedIn. Updated on October 01, Tweet Share Email. In This Article. Hexadecimal Uses. How to Count in Hexadecimal. Manually Converting Hex Values. Note also that hard-coded magic numbers are just that and it is not all that important no matter numbering system to use.

Generally the use of Hex numbers instead of Decimal it's because the computer works with bits binary numbers and when you're working with bits also is more understandable to use Hexadecimal numbers, because is easier going from Hex to binary that from Decimal to binary.

There are 8 bits in a byte. Hex, base 16, is terse. Any possible byte value is expressed using two characters from the collection Base would be more terse. Every possible byte could have its own single character, but most human languages don't use characters, so Hex is the winner.

To understand the importance of being terse, consider that back in the 's, when you wanted to examine your megabyte of memory, it was printed out in hex. The printout would use several thousand pages of big paper. Octal would have wasted even more trees. Hex, or hexadecimal, numbers represent 4 bits of data, 0 to 15 or in HEX 0 to F. Two hex values represent a byte. The radix base 10, 16, etc are ways to present those numbers in a manner that is either clearer, or more convenient.

When discussing "how many of something there are" we normally use decimal. When we are looking at addresses or bit patterns on computers, hex is usually preferred, because often the meaning of individual bytes might be important. Hex, and octal have the property that they are powers of two, so they map groupings of bit nicely. Hex maps 4 bits to one hex nibble 0-F , so a byte is stored in two nibbles FF. Octal was popular on Digital Equipment DEC and other older machines, but one octal digit maps to three bits, so it doesn't cross byte boundaries as nicely.

Overall, the choice of radix is a way to make your programming easier - use the one that matches the domain best. Looking at the file, that's some pretty groady code.

Hope you are good at C and not using it as a tutorial Hex is useful when you're directly working at the bit level or just above it. It's a compact fairly easy-to-read representation of binary. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Why use hex?

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