The TCP/IP Guide - Decimal, Binary, Octal and Hexadecimal Number Conversion

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

Decimal, Binary, Octal and Hexadecimal Numbers

Binary, Octal and Hexadecimal Arithmetic

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