Question

Determine the decimal values of the following 2's complement numbers:

(a) 0111011110
(b) 1011100111
(c) 1111111110

Answer 1

The decimal values of the 2's complement numbers are 478 for 0111011110, -137 for 1011100111, and -2 for 1111111110, following the rules of 2's complement conversion.

Step-by-step explanation:

To determine the decimal values of the given 2's complement numbers, you must first understand that in 2's complement notation, the leftmost bit indicates the sign of the number: a '0' means the number is positive, while a '1' means the number is negative.

1. For the first number, 0111011110, it starts with a '0', so it is positive. You can convert the remaining bits directly to decimal: 0111011110 in binary is 478 in decimal.
2. For the second number, 1011100111, it starts with a '1', which means it's negative. To get the positive equivalent, flip all the bits and add 1: 0100011000 in binary, then add 1 to get 0100011001, which is 137 in decimal. Since the original number was negative, the final value is -137.
3. For the third number, 1111111110, it also starts with a '1', indicating it's negative. Flip the bits to get 0000000001, then add 1 to get 0000000010, which is 2 in decimal. The final 2's complement number is -2.