The correct answer is: B. 1000 0000 0000 0111
A 16-bit signed binary number can be represented as follows:
$$N = 2^{15}x_{15} + 2^{14}x_{14} + … + 2^2x_2 + 2^1x_1 + x_0$$
where $x_i$ is the $i$th bit of the number, starting from the right, and $N$ is the value of the number.
To represent the number $-7$, we need to find the binary number that has a value of $7$ when all the bits are set to 1, and then flip the sign bit (the leftmost bit). The binary number for $7$ is $1111 1111$, so the binary number for $-7$ is $1000 0000$.
Here is a table showing the bit values for each option:
Option | Bit value
——- | ——–
A | 0000 0000 0000 0111
B | 1000 0000 0000 0111
C | 0111 0000 0000 0001
D | 0111 0000 0000 0000
E | None of the above
As you can see, only option B has the correct bit values for $-7$.