513 in Binary

Decimal 513 in binary conversion provides the detailed information on what is the binary equivalent of (513)10, and the step-by-step work for how to convert the decimal (base-10) number 513 to its binary (base-2) equivalent.

(513)10 in binary is equal to:
(513)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 513, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

513 MOD-2	513 / 2 = 256	Remainder is 1 → LSB
256 MOD-2	256 / 2 = 128	Remainder is 0
128 MOD-2	128 / 2 = 64	Remainder is 0
64 MOD-2	64 / 2 = 32	Remainder is 0
32 MOD-2	32 / 2 = 16	Remainder is 0
16 MOD-2	16 / 2 = 8	Remainder is 0
8 MOD-2	8 / 2 = 4	Remainder is 0
4 MOD-2	4 / 2 = 2	Remainder is 0
2 MOD-2	2 / 2 = 1	Remainder is 0
1 MOD-2	1 / 2 = 0	Remainder is 1 → MSB

Arrange the remainders from MSB to LSB forms the binary equivalent of 513.
513₁₀ = 1000000001₂

Hence,
513 in binary is 1000000001

where,
513₁₀ is the given decimal number,
10 in 513₁₀ represents the base-10 or decimal number system,
1000000001₂ is the binary equivalent of the decimal 41,
2 in 1000000001₂ represents the base-2 or binary number system.

Important Notes: (513)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 513 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 513 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 513 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 513 should be written from MSB to LSB to form the binary equivalent for the given decimal number (513)10.