523 in Binary

Decimal 523 in binary conversion provides the detailed information on what is the binary equivalent of (523)10, and the step-by-step work for how to convert the decimal (base-10) number 523 to its binary (base-2) equivalent.

(523)10 in binary is equal to:
(523)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 523, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

523 MOD-2	523 / 2 = 261	Remainder is 1 → LSB
261 MOD-2	261 / 2 = 130	Remainder is 1
130 MOD-2	130 / 2 = 65	Remainder is 0
65 MOD-2	65 / 2 = 32	Remainder is 1
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 523.
523₁₀ = 1000001011₂

Hence,
523 in binary is 1000001011

where,
523₁₀ is the given decimal number,
10 in 523₁₀ represents the base-10 or decimal number system,
1000001011₂ is the binary equivalent of the decimal 41,
2 in 1000001011₂ represents the base-2 or binary number system.

Important Notes: (523)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 523 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 523 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 523 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 523 should be written from MSB to LSB to form the binary equivalent for the given decimal number (523)10.