Considering the four commonly used number systems in Computer Science - Binary…
2026
Considering the four commonly used number systems in Computer Science - Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16) - answer the following questions:
(A) Can the symbol 'BAD' represent a valid number in any of these four number systems? If yes, specify the number system in which it is valid.
(B) Convert the Octal number (365)₈ into its Binary (Base 2) equivalent and write the result.
(C) Convert the Binary number (1011101)₂ into its Hexadecimal (Base 16) equivalent and write the result.
(D) Convert the fractional Binary number (1011.11)₂ into its Decimal (Base 10) equivalent and write the result.
Attempted by 94 students.
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(A) BAD is valid only in Hexadecimal/Base 16 because hexadecimal symbols are 0-9 and A-F. It is not valid in Binary, Octal, or Decimal.
(B) Convert each octal digit to 3 binary bits:
3 -> 011, 6 -> 110, 5 -> 101
So (365)_8 = 011110101_2. The leading 0 may be omitted, so 11110101_2 is also correct.
(C) Group binary digits from the right in groups of 4:
1011101 -> 0101 1101
0101 = 5 and 1101 = D
So (1011101)_2 = 5D_16. 05D_16 is also acceptable.
(D) Use positional values:
(1011.11)_2 = 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 + 1*2^-1 + 1*2^-2
= 8 + 0 + 2 + 1 + 0.5 + 0.25
= 11.75_10 = 47/4.
Final expected answers: (A) Hexadecimal/Base 16, (B) 011110101_2 or 11110101_2, (C) 5D_16, (D) 11.75_10.