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3 Answers

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Option C Is Correct.

(326.4)= 8x 3 + 81 x 2 + 80 x 6 . 8-1 x 4  = ( 214.5)10

To convert in hexa decimal i assume you already familiar with the conventional way there is also a shortcut which is only applicable if one base can be written in the power of another base eg.( r1)m  = r2 

(326.4)=  (011010110.100)2  here we expanded every digit in three bits

3 2 6 . 4
011 010 110 . 100

(011010110.100)2  = (D6.8)16    here we grouped every 4 bits ( radix point taken as reference)

0000 1101 0110 . 1000
0 D 6 . 8

NOTE : we may pad 0 bits for grouping.

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To solve this question we will apply traditional approach: (326.4)8 = 82 * 3 + 81 * 2 + 80 * 6 . 8-1 * 4 = ( 214.5)10 is decimal representation. For hexadecimal representation group binary sequence of (214.5) = (011010110.100)2 into group of 4. i.e. 0 1101 0110. 1000 (0 can be padded after decimal) this is equivalent to- (D6.8)16. So, option (C) is correct.
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1. Converting Octal to Decimal: \[3 \times 8^2 = 192\] \[2 \times 8^1 = 16\] \[6 \times 8^0 = 6\] \[4 \times 8^{-1} = 0.5\] \[ \text{Total} = 192 + 16 + 6 + 0.5 = 214.5 \] 2. Converting Octal to Hexadecimal: Group the octal digits into groups of 2, starting from the right: \(3 \ 26.4\) Convert each group to its hexadecimal equivalent: \[3 = 3\] \[26 = 1A \ (\text{16} + \text{10})\] \[4 = 4\] Combine the hexadecimal digits: \(31A.4\) Simplify the fractional part: \(0.4\) in octal is equivalent to \(0.8\) in hexadecimal Final hexadecimal representation: \(D6.8\) Therefore, the octal number \(326.4\) is equivalent to \((214.5)_{10}\) in decimal and \((D6.8)_{16}\) in hexadecimal.

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