Calculators & Converters

    Convert Decimal 15 to Binary

    (15)10 = (?)2. Decimal 15 in binary conversion provides the detailed information on what is the binary equivalent of (15)10, and the step-by-step work for how to convert the decimal (base-10) number 15 to its binary (base-2) equivalent manually.

    (15)10 in binary is equal to:
    1510 = 11112

    Hence,
    (15)10 is equivalent to (1111)2

    where,
    1510 is the given decimal number,
    10 in 1510 represents the base-10 or decimal number system,
    11112 is the binary equivalent of the decimal 41,
    2 in 11112 represents the base-2 or binary number system.

    Important Notes: (15)10 in Binary
    The below are some of the important notes to be remembered while converting the base-10 number 15 into a binary number.

    1. The initial or first remainder while performing MOD-2 operation for 15 is a Least Significant Bit (LSB).
    2. The last remainder while performing MOD-2 operation for 15 is a Most Significant Bit (MSB).
    3. The remainders of MOD-2 operation for 15 should be written from MSB to LSB to form the binary equivalent for the given decimal number (15)10.

    For decimal values other than 15, use this below tool:

    How-to: What is (15)10 in binary?

    The below step-by-step solution shows how to convert (15)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 15 forms the binary equivalent of 15.

    Solved Example:
    What is the binary equivalent of 15?

    step 1 Observe the input parameters, values and what to be found:

    Input values:
    Decimal Number = (41)10

    what to be found:
    Which binary value is equal to the decimal number 15?
    (15)10 = (?)2

    step 2 Perform successive MOD-2 operation for decimal 15, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

    Successive MOD-2 Operation for 15:
    15 MOD-2     15 / 2 = 7  Remainder is 1 → LSB
    7 MOD-2     7 / 2 = 3  Remainder is 1
    3 MOD-2     3 / 2 = 1  Remainder is 1
    1 MOD-2     1 / 2 = 0  Remainder is 1 → MSB

    step 3 Write the remainders of MOD-2 operation for 15 from MSB to LSB forms the binary equivalent for 15:
    1111
    1510 = 11112

    Therefore,
    the binary equivalent of 15 is (1111)2
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