# Convert Decimal 54 to Binary

(54)10 = (?)2. Decimal 54 in binary conversion provides the detailed information on what is the binary equivalent of (54)10, and the step-by-step work for how to convert the decimal (base-10) number 54 to its binary (base-2) equivalent manually.

__(54)10 in binary is equal to:__

54_{10} = 110110_{2}

Hence,

(54)10 is equivalent to (110110)2

__where,__

54_{10} is the given decimal number,

10 in 54_{10} represents the base-10 or decimal number system,

110110_{2} is the binary equivalent of the decimal 41,

2 in 110110_{2} represents the base-2 or binary number system.

__Important Notes: (54)10 in Binary__

The below are some of the important notes to be remembered while converting the base-10 number 54 into a binary number.

- The initial or first remainder while performing MOD-2 operation for 54 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 54 is a Most Significant Bit (MSB).
- The remainders of MOD-2 operation for 54 should be written from MSB to LSB to form the binary equivalent for the given decimal number (54)10.

## How-to: What is (54)10 in binary?

The below step-by-step solution shows how to convert (54)10 to its equivalent binary code or number. Arranging or writing the remainders from MSB to LSB of successive MOD-2 operation for decimal 54 forms the binary equivalent of 54.

__Solved Example:__

What is the binary equivalent of 54?

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 54?

(54)10 = (?)2

step 2 Perform successive MOD-2 operation for decimal 54, and mark the initial remainder as LSB and the final remainder as MSB as like the below:

__Successive MOD-2 Operation for 54:__

54 MOD-2 | 54 / 2 = 27 | Remainder is 0 → LSB |

27 MOD-2 | 27 / 2 = 13 | Remainder is 1 |

13 MOD-2 | 13 / 2 = 6 | Remainder is 1 |

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 54 from MSB to LSB forms the binary equivalent for 54:

110110

**54**

_{10}= 110110_{2}Therefore,

the binary equivalent of 54 is (110110)2