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
(21)10 is equivalent to (10101)2
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.
- The initial or first remainder while performing MOD-2 operation for 21 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 21 is a Most Significant Bit (MSB).
- 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.
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:
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:
2110 = 101012
the binary equivalent of 21 is (10101)2