**Decimal to Binary**

To Convert a decimal number to a binary number follows a straightforward method.

It involves dividing the number to be converted, say N, by 2 (since binary is in base 2), and making note of the remainder. We continue dividing the quotient (N / 2) by 2, until we reach the division of (1 / 2), also making note of all remainders.

Example 1: Convert 98 from decimal to binary.

1) Divide 98 by 2, making note of the remainder. Continue dividing quotients by 2, making note of the remainders. Also note the star (*) beside the last remainder.

Division | Remainder,R |

98 / 2 = 49 | 0 |

49 / 2 = 24 | 1 |

24 / 2 = 12 | 0 |

12 / 2 = 6 | 0 |

6 / 2 = 3 | 0 |

3 / 2 = 1 | 1 |

1 / 2 = 0 | 1* |

2) The sequence of remainders going up gives the answer. Starting from 1*, we have 1100010. Therefore, 98 in decimal is 1100010 in binary.

Example 2: Convert 21 into binary.

Division | Remainder,R |

21 / 2 = 10 | 1 |

10 / 2 = 5 | 0 |

5 / 2 = 2 | 1 |

2 / 2 = 1 | 0 |

1 / 2 = 0 | 1* |

Therefore, 21 in decimal is 10101 in binary

**Binary to Decimal**

Now, how to convert from binary to decimal number. Binary to decimal conversion follows the same steps as decimal to binary, except in reverse order. We begin by multiplying 0 x 2 and adding 1. We continue to multiply the numbers in the "results" column by 2, and adding the digits from left to right in our binary number.

Example 1: Convert 11101 from binary to decimal.

Operation | Result |

0 x 2 + 1 | 1 |

1 x 2 + 1 | 3 |

3 x 2 + 1 | 7 |

7 x 2 + 0 | 14 |

14 x 2 + 1 | 29 |

Therefore, 11101 in binary is 29 in decimal.