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Authors:
Linda Null ,julia Lobur
Chapter:
Data Representation In Computer Systems
Exercise:
Exercises
Question:15 | ISBN:9780763704445 | Edition: 3

Question

15. Use the double-dabble method to convert 102123 directly to decimal. (Hint: you have to change the multiplier.)

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Answer

To convert the number 102123 to decimal using the double-dabble method, follow these steps:

  1. Start with the binary representation of the number, which is 0001 0000 0010 0001 0010 0011 in binary.

  2. Initialize a multiplier with the value of 5 (in decimal). This is because we are dealing with 6 digits, so we will be multiplying by 5, 4, 3, 2, 1, and 0 in successive iterations.

  3. Perform the double-dabble algorithm:

    • Starting from the leftmost bit, shift each bit to the left by 1 position.
    • If the shifted bit is greater than or equal to 5 (the current multiplier), add 3 to the shifted bit.
    • Repeat this process for each bit, moving from left to right.

  4. After performing the double-dabble algorithm, the binary representation becomes: 0000 0001 0000 0000 0000 0100 in binary.

  5. Convert the binary representation to decimal:

    • Group the bits into sets of 4, starting from the rightmost side.
    • Convert each set of 4 bits to decimal.
    • The decimal representation of the binary number is 10004.

Therefore, the decimal representation of 102123 is 10004 using the double-dabble method.

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