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Table Of Contents  The TCP/IP Guide
 9  Networking Fundamentals
      9  Backgrounder: Data Representation and the Mathematics of Computing

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Decimal, Binary, Octal and Hexadecimal Numbers
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12
3
4
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Binary, Octal and Hexadecimal Arithmetic
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Decimal, Binary, Octal and Hexadecimal Number Conversion
(Page 3 of 4)

Conversions From Binary, Octal and Hexadecimal to Decimal

Conversions to and from decimal are more complicated than conversions between binary, octal and hexadecimal, because 2, 8 and 16 are powers of two but ten is not. Of the two directions, conversions to decimal are easier: you take the value of each binary, octal or hexadecimal digit, convert it to decimal, and then multiply it by the power of 2, 8 or 16 represented by the digit's place in the number. Then you add all the numbers together. I did this in the previous topic with the example of the decimal number 211 (see Table 2).

Let’s take an example of going from hexadecimal to decimal. Table 4 shows the hexadecimal number 0x830C converted to decimal (octal uses a similar process). Read the table from left to right, top to bottom; each digit’s value is multiplied by the appropriate power of 16 and added together, yielding the result 33,548 decimal.


Table 4: Hexadecimal to Decimal Number Conversion

Hexadecimal Number

8

3

0

C

Decimal Value of Digit

8

3

0

12

Power of 16

163

162

161

160

Value of Digit Place

4096

256

16

1

Value For This Number

4096*8 = 32768

3*256 = 768

0*16 = 0

12*1 = 12

Running Sum (from left to right)

32768

32768+768 = 33536

33536

33536+12 = 33548


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Decimal, Binary, Octal and Hexadecimal Numbers
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