We all know how to convert simple binary to dec and vice versa but what about hex? and what if we don’t have a calculator handy?
Let’s take a simple hex address abcd
The easiest task is to convert it to binary:
a (dec 10) is in binary 1010 because the first 1 stands for 8, next 0 stands for 4, 1 stands for 2, 0 stands for 1, so 8+2 = 10, or a in hex
b (dec 11) is in binary 1011 because the first 1 stands for 8, next 0 stands for 4, 1 stands for 2, 1 stands for 1, so 8+2 + 1= 11, or b in hex
So abcd will be:
1010101111001101
So we have a 16-digit binary number.
The first digit in a 16 digit binary number stands for 32768, next one for 16384, next one for 8192. So we have
SUM
1×32768
0x16384
1×8192 40960
0x4096
1×2048 43008
0x1024
1×512 43520
1×256 43776
1×128 43904
1×64 43968
0x32
0x16
1×8 43976
1×4 43980
0x2
1×1 43981
So abcd is 43981 in dec or 1010101111001101 in binary.
So if you don’t have a calculator handy, you can just use a piece of paper to calculate hex to binary in a few seconds and then to dec in under a minute. Obviously, some numbers will be easier to calculate than others, e.g. a000 is in binary 1010000000000000 so you know it’s simply 32768 + 16384 = 49152. It’s like with simple multiplication, where after a while you don’t need to calculate how much is 6×8, because you’ve internalized the result.
other examples:
ef
11101111
This one is very easy, because you know that 11111111 is 255, and a zero in the fifth position is 16 so it’s easier to deduct than to add. So 255-16=239.
Similarly
feff
1111111011111111
we know that ffff is 65535 and zero is in the eighth position (256). <eight because the first from the right is actually 2 to the power of 0 = 1> So feff is
65535 – 256 OR
65535 – 235 – 21 !!!easier to calculate!!!
= 65279
