“100” is a number in Octal Number System. What will be its representation in Hexadecimal Number System ?
40
40 option is correct.
Converting between positional number systems is done by going through the decimal (base-10) value as an intermediate representation: read the source string as a weighted sum of powers of its base, then rewrite that value as a weighted sum of powers of the target base.
Step 1 — the octal string "100" has place values \(1 \cdot 8^{2} + 0 \cdot 8^{1} + 0 \cdot 8^{0} = 64\) in decimal. Step 2 — convert 64 to hexadecimal by successive division by 16: \(64 = 4 \cdot 16 + 0\), giving the hex digits \(4\) and \(0\), i.e. the hex string "40".
The value 64 is the decimal representation, not the hexadecimal one. The strings 100 and 256 are unrelated to a base conversion of octal 100.
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