To convert a hexadecimal number to binary in C, you can use the following code:

#include <stdio.h> #include <string.h> // Function to convert a hexadecimal digit to its binary representation char* hexToBinary(char hexDigit) { switch (hexDigit) { case '0': return "0000"; case '1': return "0001"; case '2': return "0010"; case '3': return "0011"; case '4': return "0100"; case '5': return "0101"; case '6': return "0110"; case '7': return "0111"; case '8': return "1000"; case '9': return "1001"; case 'A': case 'a': return "1010"; case 'B': case 'b': return "1011"; case 'C': case 'c': return "1100"; case 'D': case 'd': return "1101"; case 'E': case 'e': return "1110"; case 'F': case 'f': return "1111"; default: return ""; } } // Function to convert a hexadecimal string to binary void convertHexToBinary(const char* hexString, char* binaryString) { int i, j = 0; int len = strlen(hexString); for (i = 0; i < len; i++) { char* binaryDigit = hexToBinary(hexString[i]); if (strcmp(binaryDigit, "") != 0) { strcat(binaryString, binaryDigit); j += 4; } } } int main() { char hexString[100]; char binaryString[400] = ""; // Assuming the hexadecimal string is not too large printf("Enter a hexadecimal number: "); scanf("%s", hexString); convertHexToBinary(hexString, binaryString); printf("Binary representation: %s\n", binaryString); return 0; }

Here’s how this code works:

- The
`hexToBinary`

function takes a hexadecimal digit as input and returns its binary representation as a string. It uses a switch statement to map each hexadecimal digit to its corresponding binary representation. - The
`convertHexToBinary`

function takes a hexadecimal string and a binary string as input. It iterates over each character in the hexadecimal string, calls`hexToBinary`

to convert each digit to its binary representation, and concatenates the binary digits to the binary string. - In the
`main`

function, the user is prompted to enter a hexadecimal number. The`convertHexToBinary`

function is called to convert the hexadecimal string to a binary string. - Finally, the binary string is printed as the output.

Note: This code assumes that the input hexadecimal number is valid and doesn’t perform any error handling. You may need to add additional validation if required.

### What is hexadecimal?

Hexadecimal is a number system used in mathematics and computer science. It is often referred to as “hex” for short. The hexadecimal system is based on the number 16, hence it uses 16 distinct symbols to represent numbers.

In decimal (base-10) system, we use the digits 0-9 to represent numbers. In hexadecimal, we use the digits 0-9 to represent the values 0-9, and the letters A-F (or a-f) to represent the values 10-15. This means that after 9, the letters A, B, C, D, E, and F are used to represent the values 10, 11, 12, 13, 14, and 15, respectively.

Here is a table showing the decimal and hexadecimal representations for the numbers 0-15:

Decimal | Hexadecimal |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

10 | A |

11 | B |

12 | C |

13 | D |

14 | E |

15 | F |

Hexadecimal numbers are often used in computer programming and digital systems because they can represent binary numbers in a more compact and readable format. Each hexadecimal digit represents a group of four binary digits (bits), making it easier to work with binary data.

For example, the binary number 1010 can be represented as the hexadecimal digit A. Similarly, the binary number 1111 can be represented as the hexadecimal digit F.

Hexadecimal numbers are prefixed with “0x” to indicate their base. For example, 0x2A is a hexadecimal representation of the decimal number 42.

Hexadecimal is widely used in various applications, including representing memory addresses, colors in graphics, and encoding binary data in a more human-readable form.

### What is Binary?

Binary is a number system that uses only two symbols, typically represented as 0 and 1. It is also known as the base-2 number system. In contrast to the decimal system (base-10) that humans commonly use, which uses ten digits (0-9), binary uses only two digits to represent numbers and perform arithmetic operations.

In the binary system, each digit represents a power of 2, starting from the rightmost digit. The rightmost digit has a value of 2^0 (1), the next digit to the left has a value of 2^1 (2), the next has a value of 2^2 (4), and so on. The value of each digit is calculated by multiplying the digit by the corresponding power of 2 and summing the results.

Here is a table showing the decimal and binary representations for the numbers 0-15:

Decimal | Binary |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

Binary numbers are fundamental in computer science and digital systems. They are used to represent data and perform logical operations in computer hardware and software. Binary digits, also called bits, are the building blocks of all digital information.

For example, binary is used to represent the on/off state of electronic circuits, the storage of data in computer memory, and the encoding of characters and instructions in computer programs. Binary operations such as bitwise AND, OR, and XOR are used for logical operations and manipulation of binary data.

Binary numbers can be converted to other number systems, such as decimal or hexadecimal, to make them more human-readable or for specific applications.

### Example of Hexadecimal to Binary in C:

Certainly! Here’s an example of a C program that converts a hexadecimal number to binary:

#include <stdio.h> #include <string.h> // Function to convert a hexadecimal digit to its binary representation char* hexToBinary(char hexDigit) { switch (hexDigit) { case '0': return "0000"; case '1': return "0001"; case '2': return "0010"; case '3': return "0011"; case '4': return "0100"; case '5': return "0101"; case '6': return "0110"; case '7': return "0111"; case '8': return "1000"; case '9': return "1001"; case 'A': case 'a': return "1010"; case 'B': case 'b': return "1011"; case 'C': case 'c': return "1100"; case 'D': case 'd': return "1101"; case 'E': case 'e': return "1110"; case 'F': case 'f': return "1111"; default: return ""; } } // Function to convert a hexadecimal string to binary void convertHexToBinary(const char* hexString, char* binaryString) { int i, j = 0; int len = strlen(hexString); for (i = 0; i < len; i++) { char* binaryDigit = hexToBinary(hexString[i]); if (strcmp(binaryDigit, "") != 0) { strcat(binaryString, binaryDigit); j += 4; } } } int main() { char hexString[100]; char binaryString[400] = ""; // Assuming the hexadecimal string is not too large printf("Enter a hexadecimal number: "); scanf("%s", hexString); convertHexToBinary(hexString, binaryString); printf("Binary representation: %s\n", binaryString); return 0; }

This program uses the same logic as mentioned in the previous response. It includes two functions:

- The
`hexToBinary`

function takes a hexadecimal digit as input and returns its binary representation as a string. It uses a switch statement to map each hexadecimal digit to its corresponding binary representation. - The
`convertHexToBinary`

function takes a hexadecimal string and a binary string as input. It iterates over each character in the hexadecimal string, calls`hexToBinary`

to convert each digit to its binary representation, and concatenates the binary digits to the binary string.

In the `main`

function, the user is prompted to enter a hexadecimal number. The `convertHexToBinary`

function is then called to convert the hexadecimal string to a binary string. Finally, the binary string is printed as the output.

Note that you need to input a valid hexadecimal number without any prefix like “0x”. For example, if you want to convert the hexadecimal number “2A”, you should enter “2A” as the input.