Question

Add the following decimal numbers in 2's complement

i) -12 and -18.

11) -14 from +12.

Answer 1

i) To add -12 and -18 in 2's complement, first convert the decimal numbers to their binary representation:

-12 = (0)1100 in 2's complement
-18 = (1)0002 in 2's complement

Now add the two binary numbers:

01100 (12 in binary representation)
+ 10002 (-18 in 2's complement)
_________________________
1 11110

The result in binary is 11110. Since the most significant bit is 1, indicating that it is a negative number, we convert it back to its decimal representation:

11110 in 2's complement = -30 in decimal

Therefore, -12 + -18 = -30

ii) To subtract -14 from +12, first convert the decimal numbers to their binary representation:

+12 = 01100
-14 = (1)0010 in 2's complement

Now subtract the binary numbers:

01100 (12 in binary representation)
- 10010 (-14 in 2's complement)
________________________
11010

The result in binary is 11010. Since the most significant bit is 1, indicating that it is a negative number in 2's complement, we convert it back to its decimal representation.

11010 in 2's complement = -10 in decimal

Therefore, +12 - (-14) = -10