Question

Find the double word-length 2's complement representation of each of the following decimal numbers:a. 3874

Answer 1

Answer:

-3874₁₀ = 1111 1111 1111 1111 1111 1111 1101 1110₂

Explanation:

2's complement is a way for us to represent negative numbers in binary.

To get 2's complement:

1. Invert all the bits

2. Add 1 to the inverted bits

Summary: 2's complement = -N = ~N + 1

1. Inverting the number

3874₁₀ = 1111 0010 0010₂

~3874₁₀ = 0000 1101 1101₂

2. Add 1 to your inverted bits

~3874₁₀ + 1 = 0000 1101 1101₂ + 1

= 0000 1101 1110₂

You can pad the most signigicant bits with 1's if you're planning on using more bits.

so,

12 bits                          16 bits

0000 1101 1110₂  = 1111 0000 1101 1110₂

They asked for double word-length (a fancy term for 32-bits), so pad the left-most side with 1s' until you get a total of 32 bits.

           32 bits

= 1111 1111 1111 1111 1111 1111 1101 1110