Which of the following three numbers (A-C) in decimal, octal and hexadecimal notations, respectively. is/are equivalent to (11011001)in binary notation?

(A)

(B)

(C)

Choose the correct answer from the options given below:

This question was previously asked in
UGC NET Paper 1: Held on 8th Oct 2022 Shift 1
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  1. A Only
  2. B Only
  3. A and B Only
  4. A and C Only

Answer (Detailed Solution Below)

Option 4 : A and C Only
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins

Detailed Solution

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Key Points 

  • To convert from binary to decimal, we can use the following method:
  • Starting from the right-most digit of the binary number,
  • multiply each digit by the value of 2 raised to its position (starting from 0), and then sum the results.
  • For example, to convert (11011001)2 to decimal, we can do the following:

(1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 128 + 64 + 0 + 16 + 8 + 0 + 0 + 1 = 217

  • To convert from decimal to octal or hexadecimal, we can use the following method:
  • For octal, we can divide the decimal number by 8 repeatedly and write down the remainder in reverse order. For example, to convert 217 to octal:
    • 217 ÷ 8 = 27 remainder
    • 1 27 ÷ 8 = 3 remainder
    • 3 3 ÷ 8 = 0 remainder 3
    • So, (331)8 is equivalent to (217)10.

For hexadecimal, we can divide the decimal number by 16 repeatedly and write down the remainder in reverse order,

  • using A=10, B=11, C=12, D=13, E=14, and
  • F=15 for the remainder of 10 to 15.
  • For example, to convert 217 to hexadecimal:
  • 217 ÷ 16 = 13 remainder 9 = D9
  • So, (D9)16 is equivalent to (217)10.

.Using this method, we can find that only options A and C are correct. Option B, which is (326)8 and (14A)16, is not equivalent to (11011001)2

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