Binary & Hexadecimal Math

From Binary to Decimal

Counting in binary means adding up the powers of 2 where the bits are on (meaning they are 1). Each bit position represents a power of 2, starting from the right:

1   0   0   1
8   4   2   1

Here, only 8 and 1 are on

8 + 1 = 9

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From Decimal to Binary

Let’s take the number 176 and convert it to binary. We use these positions (powers of 2):

128  64  32  16  8  4  2  1

Start from the left:

• Is 176 bigger than 128? Yes! Turn on the 128 bit (write 1)

176 - 128 = 48

1 0 0 0 0 0 0 0

• Is 48 bigger than 64? No! Bit stays 0

• Is 48 bigger than 32? Yes! Turn on the 32 bit

48 - 32 = 16

1 0 1 0 0 0 0 0

• Is 16 equal to 16? Yes! Turn on the 16 bit

 16 - 16 = 0
 
 1 0 1 1 0 0 0 0

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From Decimal to Hexadecimal

Let’s say you want to convert 100 into hexadecimal.

• Is 100 bigger than 256? → No → First hex digit is 0 → 0x0

• Now ask: how many 16s fit into 100?

We go like this:

16, 32, 48, 64, 80, 96 → that’s 6 times

So we write: 0x6. Now subtract 96 from 100 and we get 4, So the final hex value is: 0x64