Calculators & Converters

    Convert Decimal 21 to Binary

    (21)10 = (?)2. Decimal 21 in binary conversion provides the detailed information on what is the binary equivalent of (21)10, and the step-by-step work for how to convert the decimal (base-10) number 21 to its binary (base-2) equivalent manually.

    (21)10 in binary is equal to:
    2110 = 101012

    Hence,
    (21)10 is equivalent to (10101)2

    where,
    2110 is the given decimal number,
    10 in 2110 represents the base-10 or decimal number system,
    101012 is the binary equivalent of the decimal 41,
    2 in 101012 represents the base-2 or binary number system.

    Important Notes: (21)10 in Binary
    The below are some of the important notes to be remembered while converting the base-10 number 21 into a binary number.

    1. The initial or first remainder while performing MOD-2 operation for 21 is a Least Significant Bit (LSB).
    2. The last remainder while performing MOD-2 operation for 21 is a Most Significant Bit (MSB).
    3. The remainders of MOD-2 operation for 21 should be written from MSB to LSB to form the binary equivalent for the given decimal number (21)10.

    For decimal values other than 21, use this below tool:

    How-to: What is (21)10 in binary?

    The below step-by-step solution shows how to convert (21)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 21 forms the binary equivalent of 21.

    Solved Example:
    What is the binary equivalent of 21?

    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 21?
    (21)10 = (?)2

    step 2 Perform successive MOD-2 operation for decimal 21, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

    Successive MOD-2 Operation for 21:
    21 MOD-2     21 / 2 = 10  Remainder is 1 → LSB
    10 MOD-2     10 / 2 = 5  Remainder is 0
    5 MOD-2     5 / 2 = 2  Remainder is 1
    2 MOD-2     2 / 2 = 1  Remainder is 0
    1 MOD-2     1 / 2 = 0  Remainder is 1 → MSB

    step 3 Write the remainders of MOD-2 operation for 21 from MSB to LSB forms the binary equivalent for 21:
    10101
    2110 = 101012

    Therefore,
    the binary equivalent of 21 is (10101)2
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