Answer:
-3874₁₀ = 1111 1111 1111 1111 1111 1111 1101 1110₂
Step-by-step 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