(C012.25)H - (10111001110.101)B =

2007

(C012.25)H - (10111001110.101)B =

  1. A.

    (135103.412)o

  2. B.

    (564411.412)o

  3. C.

    (564411.205)o

  4. D.

    (135103.205)o

Attempted by 256 students.

Show answer & explanation

Correct answer: A

Solution (concise):

Step 1 — Convert the binary operand to octal:

  • Group binary integer part in threes from the radix point to the left: 10111001110 → 010 111 001 110

  • Map each 3-bit group to an octal digit: 010 → 2, 111 → 7, 001 → 1, 110 → 6 → integer part 2716

  • Group fractional bits to the right of the point in threes: .101 → .101 → 5 → fractional part .5

  • Therefore (10111001110.101)₂ = (2716.5)₈

Step 2 — Perform the subtraction in the same base (octal):

  • Convert the other number (the left operand) into octal if it is not already in octal. Align integer and fractional parts and subtract digit by digit using base-8 borrowing rules (borrow 1 = 8 in the next lower place).

  • Apply fractional borrows if needed across the radix point, then proceed with integer-part subtraction with borrows.

  • Carrying out these steps (using the converted value (2716.5)₈ for the binary operand) yields the result (135103.412)₈.

Check (optional):

  • You can verify the result by converting the final octal result back to binary or to decimal and ensuring that left operand − (10111001110.101)₂ equals the same decimal value.

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