Final answer:
Decimal numbers can be represented in binary using three different systems: signed magnitude, one's complement, and two's complement. Positive numbers are represented the same in all three, while negative numbers are represented differently. An 8-bit system has limitations for representing certain negative numbers. Option D is the correct answer.
Step-by-step explanation:
Converting decimal numbers into binary representations such as 8-bit signed magnitude, one's complement, and two's complement requires understanding binary number systems and how negative numbers are treated in binary. In signed magnitude, the first bit represents the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude. One's complement involves inverting all the bits of the positive version of the number to represent a negative number. Two's complement is created by inverting all the bits (like in one's complement) and then adding 1 to the least significant bit.
For example, the decimal number 77 is represented in binary as 01001101 in signed magnitude. In one's complement and two's complement, the representation is the same for positive numbers.
The decimal number -42 in binary, using signed magnitude, is 10101010. In one's complement, you invert the positive binary representation to get 11010101; add 1 for two's complement to get 11010110.
119 represented as an 8-bit binary number in signed magnitude is 01110111. As with other positive numbers, one's and two's complements are the same.
For -107, the signed magnitude representation is 110101011, however, since it's an 8-bit system, it cannot correctly represent -107 as it exceeds the bit limit. One's complement and two's complement can't be represented either due to this constraint.