What is the sum of the binary (base 2) number (1100)2 and the hexadecimal (base 16) number (3)16?

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UGC NET Paper 1: Held on 21st Oct 2022 Shift 2
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  1. (F)16
  2. (15)16
  3. (1003)10
  4. (1103)8

Answer (Detailed Solution Below)

Option 1 : (F)16
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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the correct answer is 1) (F)16,

Important Points 

To add the binary number (1100)2 and the hexadecimal number (3)16,

  • we need to convert them to the same base.
  • We can convert the hexadecimal number to binary by replacing each digit with its 4-bit binary equivalent:
  • (3)16 = (0011)2
  • Now we can add the binary numbers:
  • 1100
    • 0011
    • 1111

The result is (1111)2 in binary.

  • To convert this to hexadecimal,
  • we can group the binary digits into groups of 4, starting from the right:
  • (1111)2 = (F)16

Therefore, the sum of the binary number (1100)2 and the hexadecimal number (3)16 is (F)16. Option 1, (F)16, is the correct answer.

 
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