The following is a C program to convert a decimal number to a binary number:

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/******************************************************* Program to convert a decimal number to a binary number ******************************************************/ #include<stdio.h> // include stdio.h library #include<math.h> // include math.h library int main(void) { long long num, bin = 0; int i = 0, rem; printf("Enter a decimal number: "); scanf("%lld", &num); while(num != 0) { rem = num % 2; // get the remainder bin = rem * (long long)pow(10, i++) + bin; num /= 2; // get the quotient } printf("%lld", bin); return 0; // return 0 to operating system } |

**Expected Output:**

1sr run:

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Enter a decimal number: 4 100 |

2nd run:

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Enter a decimal number: 123456 11110001001000000 |

## How it works:

To convert a decimal number to a binary number, we follow these steps:

**Step 1**: Divide the decimal number continuously by 2 and right the remainder on the right-hand side of the dividend. We repeat this process until we get the quotient 0.

**Step 2**: Write the remainders from bottom to top.

Let’s take some examples now:

**Example 1**: Convert decimal number `5`

to a binary.

**Step 1**:

Quotient | Remainder | |
---|---|---|

`5/2` |
`2` |
`1` |

`2/2` |
`1` |
`0` |

`1/2` |
`0` |
`1` |

**Step 2**:

5_{10} = 101_{2}

**Example 2**: Convert decimal number `123`

to a binary.

**Step 1**:

Quotient | Remainder | |
---|---|---|

`123/2` |
`61` |
`1` |

`61/2` |
`30` |
`1` |

`30/2` |
`15` |
`0` |

`15/2` |
`7` |
`1` |

`7/2` |
`3` |
`1` |

`3/2` |
`1` |
`1` |

`1/2` |
`0` |
`1` |

**Step 2**:

123_{10} = 1111011_{2}

The following table shows what happens at each iteration of the loop (assuming `num = 4`

):

Iteration | rem | bin | num | i |
---|---|---|---|---|

After 1st iteration | `rem = 4 % 2 = 0` |
`bin = 0 * (10^0) + 0 = 0` |
`num = 4 / 2 = 2` |
`i = 2` |

After 2nd iteration | `rem = 2 % 2 = 0` |
`bin = 0 * (10^1) + 0 = 0` |
`num = 2 / 2 = 1` |
`i = 3` |

After 3rd iteration | `rem = 1 % 2 = 1` |
`bin = 1 * (10^2) + 0 = 100` |
`num = 1 / 2 = 0` |
`i = 4` |