Convert Decimal 23 to Binary
(23)10 = (?)2. Decimal 23 in binary conversion provides the detailed information on what is the binary equivalent of (23)10, and the step-by-step work for how to convert the decimal (base-10) number 23 to its binary (base-2) equivalent manually.
(23)10 in binary is equal to:
2310 = 101112
(23)10 is equivalent to (10111)2
2310 is the given decimal number,
10 in 2310 represents the base-10 or decimal number system,
101112 is the binary equivalent of the decimal 41,
2 in 101112 represents the base-2 or binary number system.
Important Notes: (23)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 23 into a binary number.
- The initial or first remainder while performing MOD-2 operation for 23 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 23 is a Most Significant Bit (MSB).
- The remainders of MOD-2 operation for 23 should be written from MSB to LSB to form the binary equivalent for the given decimal number (23)10.
How-to: What is (23)10 in binary?
The below step-by-step solution shows how to convert (23)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 23 forms the binary equivalent of 23.Solved Example:
What is the binary equivalent of 23?
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 23?
(23)10 = (?)2
step 2 Perform successive MOD-2 operation for decimal 23, and mark the initial remainder as LSB and the final remainder as MSB as like the below:
Successive MOD-2 Operation for 23:
|23 MOD-2||23 / 2 = 11||Remainder is 1 → LSB|
|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 23 from MSB to LSB forms the binary equivalent for 23:
2310 = 101112
the binary equivalent of 23 is (10111)2