Find the binary equivalent of (374.26)8 and the octal equivalent of (1110100.0100111)2
Answers
Answer:
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Step-by-step explanation:
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The binary equivalent of (374.26)⁸ is 11111100.01011 and the octal equivalent of (1110100.0100111)₂ is 164.234.
Given that,
We have to find the binary equivalent of (374.26)⁸ and octal equivalent of (1110100.0100111)₂.
We know that,
Each digit in octal can be represented as 3 bits in binary number
3 7 4. 2 6
011 111 100. 010 110
Therefore the binary equivalent of (346.26)⁸ is
011111100.010110
MSB on the LHS of the decimal point and LSB on the RHS of the decimal point in a binary number can be ignored.
So, (374.26)⁸ = 11111100.01011
3 bits of a binary number represent 1 octal digit
Given binary number:
1110100.0100111
For LHS of the decimal , start spliting the binary number into bits of three from Least significant bit.
As we go towards the MSB, if 3 bits are not there, add zeroes to the right. Since 0 at MSB can be ignored.
For RHS of a binary digit, start spliting the number into bits of 3 from MSB. as we go towards the LSB , add zeroes to complete 3 bits. Zeroes in LSB in the right hand side of a decimal can be ignore.
Step 1:
1 110 100. 010 011 1
Step2: since there are not enough bits in the LHS of the decimal, add zeroes in the MSB
001 110 100. 010 011 1
Step 3: since there are not enough bits in the RHS of the decimal, add zeroes in the LSB
1 00 110 100. 010 011 100
Step 4: Convert each group of three binary digits to one octal digit.
001 110 100. 010 011 100
1 6 4 . 2 3 4
So, the octal equivalent of (1110100.0100111) is 164.234
Therefore, the binary equivalent of (374.26)⁸ is 11111100.01011 and the octal equivalent of (1110100.0100111)₂ is 164.234.
To learn more about binary visit:
https://brainly.in/question/54118052
https://brainly.in/question/1519366
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