Convert Decimal 46 to Binary

(46)10 = (?)2. Decimal 46 in binary conversion provides the detailed information on what is the binary equivalent of (46)10, and the step-by-step work for how to convert the decimal (base-10) number 46 to its binary (base-2) equivalent manually.

(46)10 in binary is equal to:
46₁₀ = 101110₂

Hence,
(46)10 is equivalent to (101110)2

where,
46₁₀ is the given decimal number,
10 in 46₁₀ represents the base-10 or decimal number system,
101110₂ is the binary equivalent of the decimal 41,
2 in 101110₂ represents the base-2 or binary number system.

Important Notes: (46)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 46 into a binary number.

The initial or first remainder while performing MOD-2 operation for 46 is a Least Significant Bit (LSB).
The last remainder while performing MOD-2 operation for 46 is a Most Significant Bit (MSB).
The remainders of MOD-2 operation for 46 should be written from MSB to LSB to form the binary equivalent for the given decimal number (46)10.

For decimal values other than 46, use this below tool:

How-to: What is (46)10 in binary?

The below step-by-step solution shows how to convert (46)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 46 forms the binary equivalent of 46.

Solved Example:
What is the binary equivalent of 46?

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 46?
(46)10 = (?)2

step 2 Perform successive MOD-2 operation for decimal 46, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

Successive MOD-2 Operation for 46:

46 MOD-2	46 / 2 = 23	Remainder is 0 → LSB
23 MOD-2	23 / 2 = 11	Remainder is 1
11 MOD-2	11 / 2 = 5	Remainder is 1
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 46 from MSB to LSB forms the binary equivalent for 46:
101110
46₁₀ = 101110₂

Therefore,
the binary equivalent of 46 is (101110)2