Counting backwards in binary what happens as we go backwards

Counting backwards in binary, what happens as we go backwards from 0?

Solution

this is a good question.

lets try to understand this using an example

the binary representation of

17 is = 00010001

now if we talk about the representation of -17 into the binary form then we\'ll take the complement of the 8 bit binary code that we have stated for the integre 17

this means that every 0 in the 8 bit code of 17 will be converted into 1 likewise every 1 will be converted into 0.

and then add 1 to the new 8 bit code.

so 1 --> 0

and 0 --> 1

so the binary representation of :

17 is = 00010001
and -17 = 11101110

now add 1 to 11101110

=> 11101110

     +         1

--------------------

    11101111          , this we got using the binary addition

so if we go backwards from 0 then e\'ll encounter negative integers

like -1 , -2 , -3 , -4 ..........

so to represent them in the binary form

just form the 8 bit bnary code for the corresponding positive integer like

if its -4 then find the code for 4

then take its complement that is convert 0 to 1 and 1 to 0

and then add 1 to it using binary addition.