311 in Binary

Decimal 311 in binary conversion provides the detailed information on what is the binary equivalent of (311)10, and the step-by-step work for how to convert the decimal (base-10) number 311 to its binary (base-2) equivalent.

(311)10 in binary is equal to:
(311)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 311, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

311 MOD-2	311 / 2 = 155	Remainder is 1 → LSB
155 MOD-2	155 / 2 = 77	Remainder is 1
77 MOD-2	77 / 2 = 38	Remainder is 1
38 MOD-2	38 / 2 = 19	Remainder is 0
19 MOD-2	19 / 2 = 9	Remainder is 1
9 MOD-2	9 / 2 = 4	Remainder is 1
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 311.
311₁₀ = 100110111₂

Hence,
311 in binary is 100110111

where,
311₁₀ is the given decimal number,
10 in 311₁₀ represents the base-10 or decimal number system,
100110111₂ is the binary equivalent of the decimal 41,
2 in 100110111₂ represents the base-2 or binary number system.

Important Notes: (311)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 311 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 311 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 311 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 311 should be written from MSB to LSB to form the binary equivalent for the given decimal number (311)10.