Number Representation

Computers store data in bytes.

And 1 Byte is equal to 8 bits.

So 5 in decimal is equal to 00000101 in binary. If the sign bit is 0 we call it a positive number and if the sign bit is set (or 1) we call it a negative number.

But the problem with above approach is +0 in decimal is equal to 00000000. And -0 in decimal would be equal to 10000000.

Thats why we have twos complement.

Suppose we subtract 2 from 1

0000 0001 = 1
0000 0010 = 2

# This operation is not possible, so we borrow a bit

1 0000 0001 = now 1 becomes (256 + 1)
  0000 0010 = 2

0 1111 1111 = 255

# If the number is unsinged its 255, if its signed its -1 (as 1 - 2 = -1)

So the trick here is if you want singed value of any unsgined number just subtract it with 256 (if its a byte).

Suppose if we want a twos complement (signed number) of 255. It’s 255 - 256 = -1

And the opposite is true. If we want unsigned value of any signed number we add it with 256.

Lets say we want unsinged number of -1. Its 256 + (-1) = 255

Few other things to note is a single byte is equal to 2 nibbles (4 bits each). Total values unsigned 1 byte can hold is 2^8 (0 to 2^8 -1). And for a signed byte its from - 2^7 to +2^7 -1

Also rather than doing these calculations on calculator we can use following python3 methods to make things little bit efficient.

>>> hex(0b11101110)
'0xee'
>>> bin(0xee)
'0b11101110'
>>> int(0b11101110)
238