Calculators & Converters

    Convert Decimal 13 to Binary

    (13)10 = (?)2. Decimal 13 in binary conversion provides the detailed information on what is the binary equivalent of (13)10, and the step-by-step work for how to convert the decimal (base-10) number 13 to its binary (base-2) equivalent manually.

    (13)10 in binary is equal to:
    1310 = 11012

    Hence,
    (13)10 is equivalent to (1101)2

    where,
    1310 is the given decimal number,
    10 in 1310 represents the base-10 or decimal number system,
    11012 is the binary equivalent of the decimal 41,
    2 in 11012 represents the base-2 or binary number system.

    Important Notes: (13)10 in Binary
    The below are some of the important notes to be remembered while converting the base-10 number 13 into a binary number.

    1. The initial or first remainder while performing MOD-2 operation for 13 is a Least Significant Bit (LSB).
    2. The last remainder while performing MOD-2 operation for 13 is a Most Significant Bit (MSB).
    3. The remainders of MOD-2 operation for 13 should be written from MSB to LSB to form the binary equivalent for the given decimal number (13)10.

    For decimal values other than 13, use this below tool:

    How-to: What is (13)10 in binary?

    The below step-by-step solution shows how to convert (13)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 13 forms the binary equivalent of 13.

    Solved Example:
    What is the binary equivalent of 13?

    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 13?
    (13)10 = (?)2

    step 2 Perform successive MOD-2 operation for decimal 13, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

    Successive MOD-2 Operation for 13:
    13 MOD-2     13 / 2 = 6  Remainder is 1 → LSB
    6 MOD-2     6 / 2 = 3  Remainder is 0
    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 13 from MSB to LSB forms the binary equivalent for 13:
    1101
    1310 = 11012

    Therefore,
    the binary equivalent of 13 is (1101)2
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