Decimal - Hexadecimal
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decimal: 1532
(highest power of 16 less than 1532)
1532/16^2 = 5 (drop decimals)
5 = 1st character of hex character.
5*16^2 = 1280 (take first hex char, multiply by previous power)
1532 - 1280 = 252 (subtract from initial number)
Find highest power of 16 under 252. This is 16^1, or simply 16.
252/16 = 15 (because of how hex is, A comes after 9, then B, then C all the way to F. Then it goes 1A, etc.)
15 = F
So, 5F...
15*16 = 240
252 - 240 = 12
Highest power of 16 that is lower than 12 is 16^0, which is 1.
12/1 = 12
In hex, 12 = C.
so 5FC.
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Let's use our previous Hex, 5FC.
5 = 5
F = 15
C = 12
We have 3 elements, and counting 0, that means we must start with a power of 2.
2, 1, and 0. 3 powers.
So...
first hex number, 5
5*16^2 = 1280
Second hex number = 15
15*16^1 = 240
1280 + 240 = 1520
(notice how the powers are decreasing by 1 each time?)
Third hex number = 12
12*16^0 = 12
12 + 1520 = 1532
5FC = 1532
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Let's take the decimal number 132.
The way we're going to convert this to binary is very similar to the previous examples.
First, we want to find the greatest power of 2 that's less than 132. This would be 2^7, or 128.
132 - 128 = 4 (because we didn't get a negative value, this would be 1)
(now, divide 128 by 2)
4 - 64 = -60 = (0 in binary, because it's negative.)
4 - 32 = -28 = 0
4 - 16 = -12 = 0
4 - 8 = -4 = 0
4 - 4 = 0 = 1 (gives us 0, but it isn't a negative number, so it's a binary 1.)
0 - 2 = -2 = 0 (we subtracted that 4 from 4, and we have to keep dividing until we get the power to zero.)
0 - 1 = -1 = 0
So, 132 in binary is as follows: 10000100
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This is a bit harder to explain.
Basically , starting at the right-most character in binary, we increase by powers of 2.
For instance, let's use the previous example. 10000100. Turn it sideways, like this:
1
0
0
0
0
1
0
0
And multiply, like this.
1 * 128
0 * 64
0 * 32
0 * 16
0 * 8
1 * 4
0 * 2
0 * 1
Notice a pattern? They always multiply by 2 to increase. 4*2 = 8, 8*2 = 16, etc. The left most character in binary will be multiplied by the highest value, and the right most value in binary, multiplied by 1.
128 + 4 = 132.
