Write binary equivalent of the following octal numbers. (i) 2306 (ii) 5610 (iii) 742 (iv) 65.203

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Question

Write binary equivalent of the following octal numbers.

(i) 2306

(ii) 5610

(iii) 742

(iv) 65.203

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Answer

To write the binary equivalent of an octal number, each octal digit can be replaced with its corresponding 3-bit binary group. This method ensures accurate conversion.

(i) 2306

  • 2: 010

  • 3: 011

  • 0: 000

  • 6: 110

Therefore, $2306_8 = 010011000110_2$.

(ii) 5610

  • 5: 101

  • 6: 110

  • 1: 001

  • 0: 000

Therefore, $5610_8 = 101110001000_2$.

(iii) 742

  • 7: 111

  • 4: 100

  • 2: 010

Therefore, $742_8 = 111100010_2$.

(iv) 65.203

  • 6: 110

  • 5: 101

  • .: .

  • 2: 010

  • 0: 000

  • 3: 011

Therefore, $65.203_8 = 110101.010000011_2$.

Summary of Binary Equivalents:

  1. 2306 in binary: 010011000110

  2. 5610 in binary: 101110001000

  3. 742 in binary: 111100010

  4. 65.203 in binary: 110101.010000011

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