Final answer:
To represent the numbers 100.0 and 0.25 in floating-point format, a computer would convert them into binary scientific notation. 100.0 might be represented as 1.1001 × 26 and 0.25 as 1.0 × 2-2 in binary, aligning with the structure used for floating-point representation.
Step-by-step explanation:
To represent the numbers 100.0 and 0.25 in floating-point format, a computer would convert them into a sort of scientific notation that is suitable for binary representation. Computers use a standard format defined by the IEEE (Institute of Electrical and Electronics Engineers) for floating-point numbers, which consists of three parts: the sign, the exponent, and the mantissa.
For the number 100.0, its scientific notation is 1.0 × 102. In binary, this could be represented as 1.1001 × 26, considering that 1.1001 in binary is equivalent to 1.5625 in decimal, and when multiplied by 26 (or 64 in decimal), results in 100.0.
For the number 0.25, its scientific notation is 2.5 × 10-1, or equivalently 1.0 × 10-2. In binary, this can be represented as 1.0 × 2-2, as the binary exponential shifts the decimal two places to the left, which divides the number by 4, yielding the original number 0.25.
It's important to note that while we have represented these numbers in a base-10 form here, computers would actually use binary (base-2) for both the mantissa and the exponent. This process is how computers can handle a vast number of floating-point operations quickly and precisely.