Final answer:
A 4-bit integer can represent numbers in different binary systems: unsigned with a range from 0 to 15, sign-magnified ranging from -7 to +7, and two's complement from -8 to +7, with each system using the bits differently to encode the sign and magnitude of numbers.
Step-by-step explanation:
The question is about 4-bit integer representation in different binary systems: unsigned, sign-magnified, and two's complement. In unsigned representation, all bits contribute to the magnitude of the number, allowing for values from 0 to 15. For sign-magnified, the most significant bit (leftmost bit) represents the sign (0 for positive, 1 for negative) while the remaining bits represent magnitude, resulting in a range from -7 to +7.
Finally, two's complement uses the most significant bit as the sign: a positive number is represented normally, and to find the representation of a negative number, you invert all bits of its positive counterpart and add 1, yielding a range from -8 to +7.