Decimal 57 in binary conversion provides the detailed information on what is the binary equivalent of (57)10, and the step-by-step work for how to convert the decimal (base-10) number 57 to its binary (base-2) equivalent.

__(57)10 in binary is equal to:__

(57)_{10} = (?)_{2}

Perform successive MOD-2 operation for decimal 57, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

57 MOD-2 | 57 / 2 = 28 | Remainder is 1 → LSB |

28 MOD-2 | 28 / 2 = 14 | Remainder is 0 |

14 MOD-2 | 14 / 2 = 7 | Remainder is 0 |

7 MOD-2 | 7 / 2 = 3 | Remainder is 1 |

3 MOD-2 | 3 / 2 = 1 | Remainder is 1 |

1 MOD-2 | 1 / 2 = 0 | Remainder is 1 → MSB |

57

Hence,

57

10 in 57

111001

2 in 111001

The below are some of the important notes to be remembered while converting the base-10 number 57 into a binary number.

- The initial or first remainder while performing MOD-2 operation for 57 is a Least Significant Bit (LSB).
- The last remainder while performing MOD-2 operation for 57 is a Most Significant Bit (MSB).
- The remainders of MOD-2 operation for 57 should be written from MSB to LSB to form the binary equivalent for the given decimal number (57)10.