Q1. A particular number is written as 132 in radix-4 representation.The same number in radix-5 representation is_________.
Solution
To convert the number 132 from radix-4 representation to radix-5
representation, we can first convert it to decimal representation and then
convert it to radix-5.
132 in radix-4:
(1 * 4^2) + (3 * 4^1) + (2 * 4^0) = 16 + 12 + 2 = 30 in decimal.
Now, let's convert 30 from decimal to radix-5:
30 ÷ 5 = 6 remainder 0
6 ÷ 5 = 1 remainder 1
1 ÷ 5 = 0 remainder 1
Reading the remainders in reverse order, the number 30 in decimal is
equivalent to 110 in radix-5 representation.
So, the same number in radix-5 representation is 110.
Q2Consider a computer system with 57-bit virtual addressing using
multi-level tree-structured page tables with L levels for virtual to
physical address translation. The page size is 4 KB (1 KB = 1024 B)
and a page table entry at any of the levels occupies 8 bytes. The value
of L is________ .
Solution
Number of levels (L) = Ceiling of (Number of bits for page number / Number
of bits per level)
Number of levels (L) = Ceiling of (45 / 9) = 5
Therefore, the value of L is 5.
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