conversion of various number bases
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Thread: conversion of various number bases

  1. #1
    Senior Member
    Join Date
    Aug 2001
    Posts
    352

    Lightbulb conversion of various number bases

    well here is my first (and i hope not last) tute on AntiOnline

    how to convert between various numbering systems:

    i'll start by going from base 2 (binary) to assorted other formats and will add more as i go

    base 2 (binary)--> base 16 (hex)
    as we all know, binary uses 1's and 0's to represent numbers, and hex uses numbers from 0 - 9 and letters from A - F

    binary (2) hex (16) decimal (10) octal (8)
    0000 0 0 0
    0001 1 1 1
    0010 2 2 2
    0011 3 3 3
    0100 4 4 4
    0101 5 5 5
    0110 6 6 6
    0111 7 7 7
    1000 8 8
    1001 9 9
    1010 A 10
    1011 B 11
    1100 C 12
    1101 D 13
    1110 E 14
    1111 F 15

    to go from binary to hex, get your binary number e.g. 1111 0111
    split it into groups of four digits, if you get a group which isnt four digits, add 0's to the right side until it is 4 digits long

    now back to our example 1111 0111 becomes F7 according to the above table

    to go from hex to binary, simply refer to the above conversion chart and reverse the above procedure:
    ie F becomes 1111 and 7 becomes 0111


    to convert hex to decimal we do this:
    use the hex number codes to correspond them to decimal numbers ie f is 15, 7 is 7 etc
    and reading from right to left in powers of 16 starting from 16 ^0, 16 ^1 etc

    so F7 becomes (F x 16 ^1) + (7 x 16 ^0)
    --> (F x 16) + 7
    --> 247 decimal

    to convert decimal to hex, the easiest way i know of is to convert to binary and then convert to the hex numbers using the conversion chart above


    To make our original binary number octal, we just split the binary number into groups of 3 instead of 4

    so 11110111
    is split to 111 101 011 (hope that is right)

    then you convert your groups of 3 binary numbers to their corresponding octal's
    so 111 101 011 becomes:
    753

    to convert octal to binary, you simply reverse the above procedure and add zero's to the left side of any odd groups


    Octal to decimal uses the same idea as converting decimal to hex, convert your octal to binary, then convert the binary number to decimal


    any other parts i may have missed can be done using the above ideas and the conversion chart above, hope this is of help to someone out there

    MrLeachy

  2. #2
    Senior Member
    Join Date
    Apr 2002
    Posts
    634
    Ok, now, you can easily say me in what base my signature is converted.
    One little indication: I used the ASCII code.
    Life is boring. Play NetHack... --more--

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