15 in Binary

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.

(15)10 in binary is equal to:
(15)₁₀ = (?)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.

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

Arrange the remainders from MSB to LSB forms the binary equivalent of 15.
15₁₀ = 1111₂

Hence,
15 in binary is 1111

where,
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.

1. The initial or first remainder while performing MOD-2 operation for 15 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 15 is a Most Significant Bit (MSB).
3. 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.