Convert Decimal 13 to Binary
(13)10 = (?)2. Decimal 13 in binary conversion provides the detailed information on what is the binary equivalent of (13)10, and the step-by-step work for how to convert the decimal (base-10) number 13 to its binary (base-2) equivalent manually.
(13)10 in binary is equal to:
1310 = 11012
(13)10 is equivalent to (1101)2
1310 is the given decimal number,
10 in 1310 represents the base-10 or decimal number system,
11012 is the binary equivalent of the decimal 41,
2 in 11012 represents the base-2 or binary number system.
Important Notes: (13)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 13 into a binary number.
- The initial or first remainder while performing MOD-2 operation for 13 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 13 is a Most Significant Bit (MSB).
- The remainders of MOD-2 operation for 13 should be written from MSB to LSB to form the binary equivalent for the given decimal number (13)10.
How-to: What is (13)10 in binary?
The below step-by-step solution shows how to convert (13)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 13 forms the binary equivalent of 13.Solved Example:
What is the binary equivalent of 13?
step 1 Observe the input parameters, values and what to be found:
Decimal Number = (41)10
what to be found:
Which binary value is equal to the decimal number 13?
(13)10 = (?)2
step 2 Perform successive MOD-2 operation for decimal 13, and mark the initial remainder as LSB and the final remainder as MSB as like the below:
Successive MOD-2 Operation for 13:
|13 MOD-2||13 / 2 = 6||Remainder is 1 → LSB|
|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|
step 3 Write the remainders of MOD-2 operation for 13 from MSB to LSB forms the binary equivalent for 13:
1310 = 11012
the binary equivalent of 13 is (1101)2