(C012.25)H - (10111001110.101)B =
2007
(C012.25)H - (10111001110.101)B =
- A.
(135103.412)o
- B.
(564411.412)o
- C.
(564411.205)o
- 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.