638 in Binary

Decimal 638 in binary conversion provides the detailed information on what is the binary equivalent of (638)10, and the step-by-step work for how to convert the decimal (base-10) number 638 to its binary (base-2) equivalent.

(638)10 in binary is equal to:
(638)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 638, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

638 MOD-2	638 / 2 = 319	Remainder is 0 → LSB
319 MOD-2	319 / 2 = 159	Remainder is 1
159 MOD-2	159 / 2 = 79	Remainder is 1
79 MOD-2	79 / 2 = 39	Remainder is 1
39 MOD-2	39 / 2 = 19	Remainder is 1
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 638.
638₁₀ = 1001111110₂

Hence,
638 in binary is 1001111110

where,
638₁₀ is the given decimal number,
10 in 638₁₀ represents the base-10 or decimal number system,
1001111110₂ is the binary equivalent of the decimal 41,
2 in 1001111110₂ represents the base-2 or binary number system.

Important Notes: (638)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 638 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 638 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 638 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 638 should be written from MSB to LSB to form the binary equivalent for the given decimal number (638)10.