Binary To Decimal Conversions Made Easy

Calculate Binary into Decimal

This is just a simpler way to convert from Binary to Decimal

Step one: Start off by making the following type of graph on paper


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Let us first start off simple we want to convert 0101 0110 into decemal
We go about this in the following way


Power 7 6 5 4 3 2 1 0

|2|2|2|2|2|2|2|2|
---------------------
|0|1|0|1|0|1|1|0|

The 1's are on and the 0's are off

Now we look at everything that is on so we have

2 to the 6th Power = 64
2 to the 4th Power = 16
2 to the 2nd Power = 4
2 to the 1st Power = 2

Add these up to get our decimal #

Decimal = 86

Now this was a simple one to give you an idea but its really easy just takes some time.

This is the first installment I will be going into further details later on how to change between HEX to Decimal and any way you want.

Let me know what you want to see if, also post Math questions here. I might be able to help.

how to change between hex to decimal, binary to hex

also a website convertor .... very easy :)

http://dogbert.comsc.ucok.edu/~mcdaniel/bin-dec.html (for firedevil also available bin to hex .... )

also useful website : http://www.htservices.com/Reference/...emConversions/

For all possible hex/dec/oct/bin conversions (got nice interface and sounds too) :
http://www.antionline.com/showthread...hreadid=234108

Peace always,
<jdenny>

I realize it is trivial to find a program to do this for you, but the mental exercise is good for you.
I remember my 11th grade math teacher who rarely let us use calculators, and would prefer we spend extra time doing it ourselves. In the end, I have to say I hated it and use a calculator every chance I get now.

(An interesting side note, this math teacher could do logs and decimal exponents in his head, to 3 or 4 decimal places faster than I could type them into my calculator, and he rarely missed by more than .001)

Binary to hex and vice versa is pretty easy:

Rule 1: each digit in hex takes 4 in binary

This means that dividing the length of the binary number and rounding up will give you the length of the hex number (which is more useful as a check than anything else)

Rule 2: Start at the right, and in groups of 4, convert to hex.

Hex Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
a (10) 1010
b (11) 1011
c (12) 1100
d (13) 1101
e (14) 1110
f (15) 1111

If you do the conversion a lot, it's pretty easy to remember the pattern.

Then just string them together, keeping them in order.
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Going from decimal to binary is not too hard too, just need to know those powers of 2.

1: Start with the power of 2 just below the number (the next one would be above it)

2: Subtract that from the decimal number and write down a 1

3: Then divide the power of 2 by 2 (take the next lower one)

If the decimal is higher than the power of 2, repeat the steps above

Otherwise divide the power by 2 and write down a 0, until the decimal is higher than the power, and then repeat the steps

(This is a crappy wording, so I'll provide an example)

Take the number 587.
the power of 2 directly below it is 512.
587 - 512 = 75
Binary number = 1...
512/2 = 256
Since 256>75, Binary number = 10...
256/2 = 128
Since 128>75, Binary number = 100...
128/2 = 64
Since 64<75 (go to step2)
75 - 64 = 11
Binary number = 1001...
64/2 =32
Since 32>11, Binary number = 10010...
32/2 = 16
Since 16>11, Binary number = 100100...
16/2 = 8
Since 8<11 (go to step2)
Binary number = 1001001...
11 - 8 = 3
8/2 = 4
since 4>3, Binary number = 10010010...
4/2 = 2
since 2<3 (go to step 2)
3-2 = 1
binary number = 100100101...
2/2 = 1
Therefore binary number = 1001001011

(Sorry about the length, I got carried away!)

A little easier than using a website.
If you are running windows, goto run, 'calc'. [view] > [scientific]
Now you have a full featured calculator/converter between hex, decimal, and binary.

a(sna I think you explained it very well.
I think now anyone who reads this should get the general idea and should be able to figure it out.

Thanks for the help

As I was kindly reminded, I realize I should have posted my extension as a new tut. but when I started, I didn't think it would be that long! It wont happen again :)

Actually prolly neither of these should be posted as new tutorials... I won't neg ya for it, however I was before when I first posted a tutorial. There are already at least 2 tutorials on this topic. You should search the tutorials form first to see if the information is already there (or check Negative's Tutorial Index). Posting the exact same tutorial as someone else except with different wording, regardless of whether or not it's your own material, is a waste of time. Anyways it's good to see ya have the concept down pat, just next time take a look. Remember the idea of AO isn't to raise your tutorial count, it's to post quality information, and reposted info isn't of good quality.

That's very good, when any of you figure out how to change to BCD, then u can use the alternative to ASCII.

(But who would want to?)

nice tut, but next time search the AO forums, and notice that there are like 30 tutorials over this already :)