Please Whitelist This Site? I know everyone hates ads. But please understand that I am providing premium content for free that takes hundreds of hours of time to research and write. I don't want to go to a pay-only model like some sites, but when more and more people block ads, I end up working for free. And I have a family to support, just like you. :) If you like The TCP/IP Guide, please consider the download version. It's priced very economically and you can read all of it in a convenient format without ads. If you want to use this site for free, I'd be grateful if you could add the site to the whitelist for Adblock. To do so, just open the Adblock menu and select "Disable on tcpipguide.com". Or go to the Tools menu and select "Adblock Plus Preferences...". Then click "Add Filter..." at the bottom, and add this string: "@@||tcpipguide.com^$document". Then just click OK. Thanks for your understanding! Sincerely, Charles Kozierok Author and Publisher, The TCP/IP Guide

NOTE: Using software to mass-download the site degrades the server and is prohibited. If you want to read The TCP/IP Guide offline, please consider licensing it. Thank you.

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

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic

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

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic

If you find The TCP/IP Guide useful, please consider making a small Paypal donation to help the site, using one of the buttons below. You can also donate a custom amount using the far right button (not less than $1 please, or PayPal gets most/all of your money!) In lieu of a larger donation, you may wish to consider purchasing a download license of The TCP/IP Guide. Thanks for your support! Donate $2 Donate $5 Donate $10 Donate $20 Donate $30 Donate: $

---

Home - Table Of Contents - Contact Us

The TCP/IP Guide (http://www.TCPIPGuide.com)
Version 3.0 - Version Date: September 20, 2005

© Copyright 2001-2005 Charles M. Kozierok. All Rights Reserved.
Not responsible for any loss resulting from the use of this site.