Final answer:
To represent an offset within a box in a paged virtual memory, you would need 8 bits of space.
Step-by-step explanation:
To determine the number of bits necessary to represent an offset within a box, we need to find the number of bits needed to represent the number of words in a box. Each page has 1024 words, and it is divided into 4 sandboxes. So, each sandbox contains 1024/4 = 256 words. To represent 256 words, we need log2(256) = 8 bits. Therefore, the number of bits necessary to represent an offset within a box is 8 bits.