Final answer:
Option A: The number of bits required for representing the decimal integers 0-127, 0-500, and 0-1000 are 7, 9, and 10 bits, respectively, because they are the smallest powers of two that are larger than the maximum number in each range.
Step-by-step explanation:
To represent decimal integers in binary form, we need to determine the number of bits required for each range.
a. To represent numbers from 0 to 127, we need 7 bits. This is because 2^7 = 128, so we need 7 bits to represent all the numbers from 0 to 127.
b. To represent numbers from 0 to 500, we need 9 bits. This is because 2^9 = 512, so we need 9 bits to represent all the numbers from 0 to 500.
c. To represent numbers from 0 to 1000, we need 10 bits. This is because 2^10 = 1024, so we need 10 bits to represent all the numbers from 0 to 1000.
To determine how many bits per word are needed to represent certain ranges of decimal integers, you'll need to find the smallest power of two that is equal to or greater than one more than the maximum number to represent, because you start counting from zero.