Method 2

Introduction
How Data is Stored
Text Data
Unsigned Numbers
- Base-10
- Base-2
- Base-n
Binary Addition
Signed Numbers
- Excess Notation
- Two's Complement Notation
Mapping Notations
Binary Fractions
Rational Numbers
Practice Material
- #1
- #2 - 5
- #6 - 10
- #11 - 15
- #17 - 20
- #21 - 24
- #25 - 29
- #30 - 32
- #33 - 36
- #37 - 39
- #40
- #41 - 44
- #45 - 46
- #47
- #48 - 51
- Solutions

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!