# Convert Decimal 42 to Binary

(42)10 = (?)2. Decimal 42 in binary conversion provides the detailed information on what is the binary equivalent of (42)10, and the step-by-step work for how to convert the decimal (base-10) number 42 to its binary (base-2) equivalent manually.

(42)10 in binary is equal to:
4210 = 1010102

Hence,
(42)10 is equivalent to (101010)2

where,
4210 is the given decimal number,
10 in 4210 represents the base-10 or decimal number system,
1010102 is the binary equivalent of the decimal 41,
2 in 1010102 represents the base-2 or binary number system.

Important Notes: (42)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 42 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 42 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 42 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 42 should be written from MSB to LSB to form the binary equivalent for the given decimal number (42)10.

For decimal values other than 42, use this below tool:

## How-to: What is (42)10 in binary?

The below step-by-step solution shows how to convert (42)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 42 forms the binary equivalent of 42.

Solved Example:
What is the binary equivalent of 42?

step 1 Observe the input parameters, values and what to be found:

Input values:
Decimal Number = (41)10

what to be found:
Which binary value is equal to the decimal number 42?
(42)10 = (?)2

step 2 Perform successive MOD-2 operation for decimal 42, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

Successive MOD-2 Operation for 42:
 42 MOD-2 42 / 2 = 21 Remainder is 0 → LSB 21 MOD-2 21 / 2 = 10 Remainder is 1 10 MOD-2 10 / 2 = 5 Remainder is 0 5 MOD-2 5 / 2 = 2 Remainder is 1 2 MOD-2 2 / 2 = 1 Remainder is 0 1 MOD-2 1 / 2 = 0 Remainder is 1 → MSB

step 3 Write the remainders of MOD-2 operation for 42 from MSB to LSB forms the binary equivalent for 42:
101010
4210 = 1010102

Therefore,
the binary equivalent of 42 is (101010)2 