421 in Binary

Decimal 421 in binary conversion provides the detailed information on what is the binary equivalent of (421)10, and the step-by-step work for how to convert the decimal (base-10) number 421 to its binary (base-2) equivalent.

(421)10 in binary is equal to:
(421)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 421, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

421 MOD-2	421 / 2 = 210	Remainder is 1 → LSB
210 MOD-2	210 / 2 = 105	Remainder is 0
105 MOD-2	105 / 2 = 52	Remainder is 1
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 421.
421₁₀ = 110100101₂

Hence,
421 in binary is 110100101

where,
421₁₀ is the given decimal number,
10 in 421₁₀ represents the base-10 or decimal number system,
110100101₂ is the binary equivalent of the decimal 41,
2 in 110100101₂ represents the base-2 or binary number system.

Important Notes: (421)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 421 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 421 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 421 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 421 should be written from MSB to LSB to form the binary equivalent for the given decimal number (421)10.