Hexadecimal Number

Pronunciation: /ˌhɛk.səˈdɛs.ə.məl ˈnʌm.bər/ Explain

A hexadecimal number is a number written using the hexadecimal numeration system. The hexadecimal numeration system is a base 16 numeration system. The 16 hexadecimal digits are used:

Hexadecimal Digit	Decimal Value
0	0
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
Table 1: Hexadecimal digits

The letters used for hexadecimal digits with a value of 10 through 16 are always capital letters, never lower case letters.

The place values of hexadecimal numerals are multiples of 16, just as the place values of decimal numerals are multiples of 10.

Place	Place Value
1	160 = 1
2	161 = 16
3	162 = 256
4	163 = 4096
5	164 = 65536
6	165 = 1048576
7	166 = 16777216
8	167 = 268435456
Table 2: Hexadecimal place values.

Representations

There are several different ways that are used to identify a series of hexadecimal digits as a hexadecimal number. Some of these are:

• Literature - 0FD8₁₆ - A subscripted '16' is often appended to the hexadecimal digits to distinguish them from numerals in other bases.
• HTML - ڊ - The characters '&#x' precede the hexadecimal digits and the character ';' follows them.
• C, C#, C++ programming languages - 0x309A - The characters '0x' precede the hexadecimal digits.
• Visual basic - &H3x0F - The characters '&H' precede the hexadecimal digits.

How to convert a decimal integer to a hexadecimal integer

Converting a decimal integer to a hexadecimal integer involves several steps:

1. Find the highest hexadecimal place value;
2. Divide the decimal integer by the hexadecimal place value. Record the hexadecimal digit; and
3. Use the remainder from step 2 for the next place value.

Step	Hexadecimal	Decimal	Calculations
	Value	Value
1	n/a	12530	Convert the decimal number 12530 to hexadecimal.
2	n/a	12530	Using the table of place values above, the largest place value less than or equal to 12530 is 4096.
3	3	242	Divide 12530 by 4096. The result is 3R242. The first hexadecimal digit is 3. The next digit will be found using 242.
4	30	242	Divide 242 by 256. The result is 0R242. The second hexadecimal digit is 0. The next digit will be found using 242.
5	30F	2	Divide 242 by 16. The result is 15R2. Using the table of hexadecimal digits above, the digit for 1510 is F. The third hexadecimal digit is F. The next digit will be found using 2.
6	30F2	n/a	Since the next place value is 1, simply copy the 2 to the end of the hexadecimal number. 1253010 = 30F216
Table 3: Converting a decimal number to a hexadecimal number.

How to convert a hexadecimal integer to a decimal integer

When converting a hexadecimal integer to a decimal integer, use the decimal values of the hexadecimal digits in table 1 and the place value table, table 2.

Step	Result	Discussion
1	30F216	Convert the hexadecimal number 30F216 to decimal.
2	3, 0, 15, 2	Convert each hexadecimal digit to its value.
3	3×4096, 0×256, 15×16, 2×1	Multiply the decimal value of each digit by its place value.
4	3×4096 + 0×256 + 15×16 + 2×1 = 12530	Add the products together to get the decimal value.
Table 4: Converting a hexadecimal integer to a decimal integer.

References

1. McAdams, David E.. All Math Words Dictionary, hexadecimal digit. 2nd Classroom edition 20150108-4799968. pg 90. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Hexadecimal Number. 4/22/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/hexadecimalnumber.html.

Revision History

4/22/2019: Update equations and expressions to new format. (McAdams, David E.)
3/16/2019: Fixed powers of 16 table. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/16/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)