63 in Binary

Decimal 63 in binary conversion provides the detailed information on what is the binary equivalent of (63)10, and the step-by-step work for how to convert the decimal (base-10) number 63 to its binary (base-2) equivalent.

(63)10 in binary is equal to:
(63)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 63, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

63 MOD-2	63 / 2 = 31	Remainder is 1 → LSB
31 MOD-2	31 / 2 = 15	Remainder is 1
15 MOD-2	15 / 2 = 7	Remainder is 1
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 63.
63₁₀ = 111111₂

Hence,
63 in binary is 111111

where,
63₁₀ is the given decimal number,
10 in 63₁₀ represents the base-10 or decimal number system,
111111₂ is the binary equivalent of the decimal 41,
2 in 111111₂ represents the base-2 or binary number system.

Important Notes: (63)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 63 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 63 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 63 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 63 should be written from MSB to LSB to form the binary equivalent for the given decimal number (63)10.