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Question

Convert decimal number 26.85 into binary equivalent.

The correct answer is

11010.110110

To convert the decimal number 26.85 into its binary equivalent, follow these steps:

  1. Convert the integer part (26):
    • Divide the integer part by 2 and record the remainder.
    • Continue dividing the quotient by 2 until the quotient is zero.
    • Write down the remainders in reverse order.

    26 ÷ 2 = 13 remainder 0
    13 ÷ 2 = 6 remainder 1
    6 ÷ 2 = 3 remainder 0
    3 ÷ 2 = 1 remainder 1
    1 ÷ 2 = 0 remainder 1

    Writing in reverse order gives: 11010

  2. Convert the fractional part (0.85):
    • Multiply the fractional part by 2.
    • Record the integer part of the result (0 or 1).
    • Use the new fractional part for the next iteration.
    • Repeat until the fractional part becomes zero or until the desired precision is achieved.

    0.85 x 2 = 1.70 → Integer part = 1 (Fractional part = 0.70)
    0.70 x 2 = 1.40 → Integer part = 1 (Fractional part = 0.40)
    0.40 x 2 = 0.80 → Integer part = 0 (Fractional part = 0.80)
    0.80 x 2 = 1.60 → Integer part = 1 (Fractional part = 0.60)
    0.60 x 2 = 1.20 → Integer part = 1 (Fractional part = 0.20)
    0.20 x 2 = 0.40 → Integer part = 0 (Fractional part = 0.40)

    The binary fractional part stops at (0.40), giving 110110 with desired precision.

Therefore, the binary equivalent of the decimal number 26.85 is 11010.110110.

The correct answer is 11010.110110.

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Important Questions from Binary Number System

  1. Given below are two statements

    Statement I: The base of the binary number system is 2.

    Statement II: Binary addition is just like decimal addition except that the rules are much simpler.

    In light of the above statements, choose the correct answer from the options given below

  2. A-F system is used in which of the following number systems?

  3. How many unique combinations of 0's and 1's can be made with a 5-binary-digit code?

  4. Which of the following number systems uses two numbers to represent data in computer ?

  5. Which of the following is the binary equivalent of the decimal number 35 ?

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