Answer:

To find the smallest 4-bit negative number stored in its 2s complement representation, we need to understand the concept of 2s complement and how it is represented in binary.

2s Complement Representation:
In 2s complement representation, the most significant bit (MSB) is used as the sign bit. If the sign bit is 0, it represents a positive number, and if the sign bit is 1, it represents a negative number. The remaining bits represent the magnitude of the number. To obtain the 2s complement of a negative number, we invert all the bits and add 1 to the least significant bit.

4-Bit 2s Complement Representation:
In a 4-bit representation, the MSB is the sign bit, and the remaining 3 bits represent the magnitude. The range of numbers that can be represented is from -8 to +7.

Finding the Smallest 4-Bit Negative Number:
To find the smallest 4-bit negative number, we need to find the 2s complement of the positive number with the largest magnitude, which is 7.

1. Convert 7 to binary: 0111
2. Invert all the bits: 1000
3. Add 1 to the least significant bit: 1001

Therefore, the smallest 4-bit negative number stored in its 2s complement representation is 1001, which corresponds to -7 in decimal.

Options Explanation:
a) 1000: This option is incorrect because it represents -8, not the smallest negative number.
b) 0000: This option is incorrect because it represents 0, not a negative number.
c) 1111: This option is incorrect because it represents -1, not the smallest negative number.
d) 0111: This option is incorrect because it represents +7, not a negative number.

Therefore, the correct answer is option 'A' (1000) as it represents the smallest 4-bit negative number (-8) in its 2s complement representation.