The correct answer is option 'A', which states that the range of numbers that can be represented using 6-bits in signed binary number representation is -31 to 31.

To understand why this is the correct answer, let's break it down step by step:

1. Signed Binary Number Representation:
In signed binary number representation, the leftmost bit (most significant bit) is used to represent the sign of the number.
- If the leftmost bit is 0, the number is positive.
- If the leftmost bit is 1, the number is negative.

2. 6-Bits Representation:
In a 6-bit representation, there are 6 binary digits available to represent a number.

3. Range Calculation:
Since the leftmost bit represents the sign, we have only 5 bits available to represent the magnitude of the number.
- With 5 bits, we can represent numbers from 0 to (2^5)-1, which is 0 to 31 in decimal.

4. Signed Range:
In signed binary representation, we need to consider both positive and negative ranges.
- With 5 bits, we can represent positive numbers from 0 to 31 (as calculated above).
- To represent negative numbers, we need to use the two's complement method. In this method, we invert all the bits and add 1 to the least significant bit.
- With 5 bits, the two's complement method allows us to represent negative numbers from -1 to -31.

5. Final Range:
Combining the positive and negative ranges, the overall range of numbers that can be represented using 6-bits in signed binary number representation is -31 to 31.

Therefore, the correct answer is option 'A', which states that the range of numbers that can be represented using 6-bits in signed binary number representation is -31 to 31.