If (L)_m represents a number L in base-M number system, then identify the correct ascending order of the following numbers A-D when converted to decimal number system.

A. (11001.11)₂

B. (123.2)₄

C. (31.5)₈

D. (19.6)₁₆

Choose the correct answer from the options given below:

The correct answer is - D, C, A, B

Key Points

• Base-2 to Decimal Conversion
  • (11001.11)₂ = 1*2⁴ + 1*2³ + 0*2² + 0*2¹ + 1*2⁰ + 1*2^-1 + 1*2^-2
  • = 16 + 8 + 1 + 0.5 + 0.25 = 25.75
• Base-4 to Decimal Conversion
  • (123.2)₄ = 1*4² + 2*4¹ + 3*4⁰ + 2*4^-1
  • = 16 + 8 + 3 + 0.5 = 27.5
• Base-8 to Decimal Conversion
  • (31.5)₈ = 3*8¹ + 1*8⁰ + 5*8^-1
  • = 24 + 1 + 0.625 = 25.625
• Base-16 to Decimal Conversion
  • (19.6)₁₆ = 1*16¹ + 9*16⁰ + 6*16^-1
  • = 16 + 9 + 0.375 = 25.375

Additional Information

• Understanding Number Systems
  • Binary System (Base-2)
    • Uses digits 0 and 1.
    • Each digit represents an increasing power of 2.
  • Quaternary System (Base-4)
    • Uses digits 0, 1, 2, and 3.
    • Each digit represents an increasing power of 4.
  • Octal System (Base-8)
    • Uses digits 0 to 7.
    • Each digit represents an increasing power of 8.
  • Hexadecimal System (Base-16)
    • Uses digits 0 to 9 and letters A to F.
    • Each digit represents an increasing power of 16.
• Conversion Techniques
  • To convert from any base to decimal, multiply each digit by its base raised to the power of its position and sum the results.
  • To convert from decimal to another base, repeatedly divide the decimal number by the new base and record the remainders.