Express -7 as 16-bit signed binary numbers. 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

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