105 in Binary

Decimal 105 in binary conversion provides the detailed information on what is the binary equivalent of (105)10, and the step-by-step work for how to convert the decimal (base-10) number 105 to its binary (base-2) equivalent.

(105)10 in binary is equal to:
(105)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 105, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

105 MOD-2	105 / 2 = 52	Remainder is 1 → LSB
52 MOD-2	52 / 2 = 26	Remainder is 0
26 MOD-2	26 / 2 = 13	Remainder is 0
13 MOD-2	13 / 2 = 6	Remainder is 1
6 MOD-2	6 / 2 = 3	Remainder is 0
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 105.
105₁₀ = 1101001₂

Hence,
105 in binary is 1101001

where,
105₁₀ is the given decimal number,
10 in 105₁₀ represents the base-10 or decimal number system,
1101001₂ is the binary equivalent of the decimal 41,
2 in 1101001₂ represents the base-2 or binary number system.

Important Notes: (105)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 105 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 105 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 105 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 105 should be written from MSB to LSB to form the binary equivalent for the given decimal number (105)10.