The hexadecimal (base 16) number system operates the same way as the decimal(base 10) number system, except it is based upon sixteen rather of ten. Theoperation that the decimal device is familiar.

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The 4-digit base-10 number 5826 shows up below, indicating just how the valueof the number is obtained from the values of that is 4 digits.


Everybody knows the 5826 method five-thousand eight-hundred twenty-six. Butonly since they have actually been taught that 1, 10, 100, and 1000 are part of thecalculation even though castle are never written. All the is actuallywritten is a full of twenty-one (5 and 8 and 2 and also 6). Only the interpretationthat civilization supply, which is completely mental and also unwritten, educates what iswritten through its plan value.

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Hexadecimal operates the very same way. Each digit is "weighted" through a"multiplier," through the outcomes all added together. The multipliers inboth systems room the strength of the device base (10 or 16). The strength of 10 are1, 10, 100, 1000, etc. If those of 16 space 1, 16, 256, 4096, etc. Therefore the samedigits "5826" provided in basic 16 represent a worth calculated together follows:


Though the digits space the exact same (5826) the values come out rather different,because the base and its "multiplier values" space different.

You will see hexadecimal numbers few of whose digits are letters rather ofnumbers. That"s because the variety of digits needed by any number mechanism is thenumber"s base. So basic base 2 demands 2 digits, base 10 demands 10, and base16 needs 16. Basic 2 has 0 and also 1. Basic 10 has actually 0 v 9. Basic 16 lend 0though 9 yet needs one more 6. For those, we could invent some symbols. However,for convenience we employ the an initial 6 letter of the alphabet (A v F)instead. When we operation out of number at 9, we use A together the following digit. Therefore Arepresents the value 10. B comes next, and represents 11. The hexadecimal digitsand thevalue they stand for are:

Hexadecimal digit Value


1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
A 10
B 11
C 12
D 13
E 14
F 15

Here"s the derivation of the worth of one more 4-digit hexadecimal number, butthis one uses some of the high-order number A-F:


The highest possible you deserve to count v a given variety of digits (in any type of numbersystem) is the number in i m sorry every digit has the maximum value in thenumber device (1 in base 2, or 9 in basic 10, or F in basic 16). For this reason the largestnumber you deserve to represent through 4 number in basic 16 is:


Counting any higher than the would require that girlfriend utilize an ext digits. Thevery following number is 10000 in hexadecimal, or 65536 in decimal. The is awell-known worth in computer system science and also is referred to as "64K."