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
(15)10 is equivalent to (1111)2
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.
- The initial or first remainder while performing MOD-2 operation for 15 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 15 is a Most Significant Bit (MSB).
- 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.
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:
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:
1510 = 11112
the binary equivalent of 15 is (1111)2