hexadecimal numbers.pdf

8/14/2019 Hexadecimal numbers.pdf

1/5

3/5/13 Hexadecimal numbers

homepage.smc.edu/morgan_david/cs40/hex-system.htm 1/5

Hexadecimal Number System

The hexadecimal (base 16) number system operates the same way as the decimal (base 10) number

system, except it is based on sixteen instead of ten. The operation of the decimal system is familiar.

The 4-digit base-10 number 5826 appears below, indicating how the value of the number is derived fromthe values of its 4 digits.

Everybody knows that 5826 means five-thousand eight-hundred twenty-six. But only because they havebeen taught that 1, 10, 100, and 1000 are part of the calculation even though they are never written. All that

is actually written is a total of twenty-one (5 and 8 and 2 and 6). Only the interpretation that people

supply, which is purely mental and unwritten, informs what is written with its intended value.

Hexadecimal operates the same way. Each digit is "weighted" by a "multiplier," with the results all added

together. The multipliers in both systems are the powers of the system base (10 or 16). The powers of 10

are 1, 10, 100, 1000, etc. while those of 16 are 1, 16, 256, 4096, etc. So the same digits "5826" used in base16 represent a value calculated as follows:


2/5



Though the digits are the same (5826) the values come out quite different, because the base and its"multiplier values" are different.

You will see hexadecimal numbers some of whose digits are letters instead of numbers. That's because

the number of digits needed by any number system is the number's base. So base base 2 needs 2 digits,

base 10 needs 10, and base 16 needs 16. Base 2 has 0 and 1. Base 10 has 0 through 9. Base 16 borrows 0though 9 but needs another 6. For those, we could invent some symbols. However, for convenience we

employ the first 6 letters of the alphabet (A through F) instead. When we run out of digits at 9, we use A as

the next digit. So A represents the value 10. B comes next, and represents 11. The hexadecimal digits andthevalue they stand for are:

Hexadecimal

digitValue

0 0

1 1

2 2


3/5



3 3

4 4

5 5

6 6

7 78 8

9 9

A 10

B 11

C 12

D 13E 14

F 15

Here's the derivation of the value of another 4-digit hexadecimal number, but this one uses some of the

high-order digits A-F:


4/5



The highest you can count with a given number of digits (in any number system) is the number in whichevery digit contains the maximum value in the number system (1 in base 2, or 9 in base 10, or F in base

16). So the largest number you can represent with 4 digits in base 16 is:


5/5

hexadecimal numbers.pdf

Documents