Method 2

  • Method #1 involves several steps that can be prone to error for many of us.
  • Alternatively, the following rule may be applied to find the signed complement of an original 2's complement number without doing the arithmetic involved in the conversion technique above.

Short-Cut Rule for 2's Complement Number Conversion:

Copy the digit(s) of the original number from right to left (from the least significant digit) up-to-and-including the first instance of a "1", then complement (flip) the rest of the number.



1001

  • Original 2's Complement number.

1

  • Copy the digit(s) from right to left up-to-and-including the fist occurrence of a "1" - In this case the right-most bit happens to be the fist instance of 1; so we copy (up-to-and-including) it; then stop copying.

0111

  • Now, complement (flip) the rest of the number, i.e., 0 becomes 1 and 1 becomes 0.
  • The resulting number has a sign bit of 0 so simply sum up the rest of the digits and express it as +7.

As if by magic, all that is left for us to do is to evaluate the result; express value's decimal equivalent and remember the sign."

0111 = +7...

so we can deduce that the original number represented -7... It's that simple!