Which of the following three numbers (A-C) in decimal, octal and hexadecimal notations, respectively. is/are equivalent to (11011001)₂ in binary notation?

(A) \((217)_{10}\)

(B) \((661)_{8}\)

(C) \((D9)_{16}\)

Choose the correct answer from the options given below:

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