Calculators & Converters

    Convert Decimal 48 to Binary

    (48)10 = (?)2. Decimal 48 in binary conversion provides the detailed information on what is the binary equivalent of (48)10, and the step-by-step work for how to convert the decimal (base-10) number 48 to its binary (base-2) equivalent manually.

    (48)10 in binary is equal to:
    4810 = 1100002

    Hence,
    (48)10 is equivalent to (110000)2

    where,
    4810 is the given decimal number,
    10 in 4810 represents the base-10 or decimal number system,
    1100002 is the binary equivalent of the decimal 41,
    2 in 1100002 represents the base-2 or binary number system.

    Important Notes: (48)10 in Binary
    The below are some of the important notes to be remembered while converting the base-10 number 48 into a binary number.

    1. The initial or first remainder while performing MOD-2 operation for 48 is a Least Significant Bit (LSB).
    2. The last remainder while performing MOD-2 operation for 48 is a Most Significant Bit (MSB).
    3. The remainders of MOD-2 operation for 48 should be written from MSB to LSB to form the binary equivalent for the given decimal number (48)10.

    For decimal values other than 48, use this below tool:

    How-to: What is (48)10 in binary?

    The below step-by-step solution shows how to convert (48)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 48 forms the binary equivalent of 48.

    Solved Example:
    What is the binary equivalent of 48?

    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 48?
    (48)10 = (?)2

    step 2 Perform successive MOD-2 operation for decimal 48, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

    Successive MOD-2 Operation for 48:
    48 MOD-2     48 / 2 = 24  Remainder is 0 → LSB
    24 MOD-2     24 / 2 = 12  Remainder is 0
    12 MOD-2     12 / 2 = 6  Remainder is 0
    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 48 from MSB to LSB forms the binary equivalent for 48:
    110000
    4810 = 1100002

    Therefore,
    the binary equivalent of 48 is (110000)2
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