Binary Numbers : Two's Complement

Question

i have make an exercice but i'm not sure thanks to help me :

11001011 on 8 binary digits.

Questions :

• What is the representation signed in two's complement ? i'm not sur i have make this

i reverse : 00110100 , + 1 : 00110101

• In the case of representation signed in two's complement, what is its representation of the absolute value?

Maybe still 00110101

Answer 1

In two's-complement representation, positive numbers are simply represented as themselves, and negative numbers are represented by the two's complement of their absolute value.

In two's-complement representation, a number is negative if (and only if) the highest bit is set.

So, if you want to get the absolute value, you reverse the two-complement operation only if the highest bit is set.

Example

For example, using 8 bits, the number 5 is represented as

00000101

The highest bit is 0, so it represents a positive number. To convert it to -5 in two's-complement notation, invert it and add 1:

~00000101 + 1 = 11111010 + 1 = 11111011

To take its absolute value, check if the highest bit is set (it is), and undo the two's-complement operation, that is, subtract 1 and invert bits:

~(11111011 - 1) = ~11111010 = 00000101 = 5

If the highest bit is 0, then it is a positive number, and it already is its absolute value.