Decimal to Binary Conversion Help. :-(

K1LLSW1TCH

K1LLSW1TCH

K1LLSW1TCH

Caporegime
Joined
12 Mar 2009
Posts
26,776
Hello there. Well, I've been introduced to Binary, Hexidecimal and Octal number systems and I'm very confused. My confusion begins at converting a Decimal base 10 number into a binary number. My tutor has shown me several examples and I still don't get it, it just hurts my head looking at the question and it's really frustrating not knowing where to begin. I've had a quick Google, and my tutor will e-mail me with some notes later on this evening. I'm going to fall behind if I can't get my head around converting and I just need someone to explain it to me very simply if possible. I know that this is probably a piece of cake for most of you guys, I'm not dull, I'm just **** at math.

Anyway, hopefully somebody will be able to give me a hand, cheers in advance, and no " Google Binary Conversion" posts please because they just aren't constructive and it isn't what I'm asking for.

:)
 
Your example is confusing me, if you gave me a number I wouldn't know how to put it into a binary form just by looking at yours. Where do you start when converting? What's the easiest method? And could you please describe the method that you've just demonstrated. I know I'm a pain in the ass but I'm just trying to understand your method. :(
 
(Just in case the previous post wasn't enough)

It might help to remember how decimal works:

The number 42 means 4*10 + 2*1
The number 342 means 3*100 + 4*10 + 2*1

Each digit is 10x more/less 'valuable' than the next, hence why its call decimal. So, if you want to convert from decimal to binary, the crude way to think of it is:

If the number is 42, find the largest power of 2 number smaller than it. So, start at 1, keep doubling until you get too big and go back one. So imagine it writen like this:

Code: 
42:  32 16 8 4 2 1

Now put a one under the largest one:

Code: 
42:  32 16 8 4 2 1
      1

Now subtract that number from it. 42-32 is 10

Code: 
10:  32 16 8 4 2 1
      1

Now repeat putting a one under the largest one that is still smaller, and subtract again:

Code: 
2:  32 16 8 4 2 1
     1    1

Finally this becomes:

Code: 
0:  32 16 8 4 2 1
     1    1   1

And you have got to 0, so your done. Put zeros under the rest:

Code: 
0:  32 16 8 4 2 1
     1  0 1 0 1 0

So the answer is: 101010

Did I make things better or worse? :)
 
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Binary works by expressing numbers as sums of powers of 2. So – for any number up to 255 – you need to work out how to express a the number in question as a sum of 128 (2^7), 64 (2^6), 32 (2^5), all the way down to 1 (2^0).

So, for example, 87 can be expressed as 64 + 16 + 4 + 2 + 1.

For each of these terms, we write them out as powers of 2:

64 = 2^6 (6 bits from the right)
16 = 2^4 (4 bits from the right)
4 = 2^2 (2 bits from the right)
2 = 2^1 (1 bit from the right)
1 = 2^0 (0 bits from the right, i.e. the rightmost bit)

So to construct the binary representation of the number, we just set the corresponding bits to 1, and all the rest to 0:

87 (decimal) = 1010111 (binary)

Hope that helps!
 
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I used the following method for exams:

Say you need to convert 99. If you could only make one binary digit high, what's the closest you can get to 99?

64: 1000000

What's the closest you can get to 35 (99 minus 64) if you could only make one binary digit high?

32: 0100000

What's the closest you can get to 3 (35 minus 32) if you could only make one binary digit high?

2: 0000010

What's the closest you can get to 1 (3 minus 2) if you could only make one binary digit high?

1: 0000001

Now do simple binary addition:

1000000
0100000
0000010
0000001

becomes 1100011

99 = 1100011

if you need it as a byte then just add a 0 onto it: 01100011
 
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Thanks you lot. Caustic, that really, really helped, and I'm off to make a cup of tea, have a sit down and then try some sums of my own. That seems quite simple in the way that you explained it and my head isn't hurting so much now. :D
 
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