# 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:__

23_{10} = 10111_{2}

Hence,

(23)10 is equivalent to (10111)2

__where,__

23_{10} is the given decimal number,

10 in 23_{10} represents the base-10 or decimal number system,

10111_{2} is the binary equivalent of the decimal 41,

2 in 10111_{2} 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:

__Input values:__

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:

10111

**23**

_{10}= 10111_{2}Therefore,

the binary equivalent of 23 is (10111)2