Question

Write a function that reads a number in binary form and converts it into hexadecimal form. Hexa-decimal values must be stored also.

Short answer

Build a function that converts binary to decimal, then to hexadecimal, and stores the result.

Step-by-step solution

Understand the Problem

To solve the problem, we need to create a function that takes a binary number as input and converts it into a hexadecimal number. Binary is base 2, and hexadecimal is base 16, so we will have to do the conversion properly. The result should be stored, likely in a variable or data structure, for later use. Let's break it down further.

Convert Binary to Decimal

The first step in converting a binary number to a hexadecimal number is to convert the binary number to its decimal (base 10) equivalent. This can be done by weighting each bit by powers of 2. For example, the binary number '1011' is converted to decimal as follows: $1\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0=8+0+2+1=11$. In Python, this can be achieved using the `int()` function, like `int(binary_number, 2)`.

Convert Decimal to Hexadecimal

Once we have the decimal representation, we convert it to hexadecimal. Hexadecimal uses digits 0-9 and letters A-F. This conversion turns the decimal number into a string of hexadecimal digits. In Python, this is easily done using the `hex()` function, followed by removing the '0x' prefix that Python adds, giving the hexadecimal representation.

Implement the Conversion Function

Now that the logic is clear, we can implement the function. It should take a binary string as input, convert it to decimal using `int(binary_number, 2)`, then convert the decimal to hexadecimal using `hex(decimal_number)`. Finally, store the hexadecimal value as a string without the '0x' prefix.

Store the Hexadecimal Value

After conversion, ensure the hexadecimal value is stored for future use. It could be stored in a variable or part of a data structure, such as a list or dictionary, if multiple values are to be recorded. For a single function call, returning the hex value might suffice.

Test the Function

Test the function with different binary inputs to ensure its correctness. For example, test with '1011' to check if it returns 'B', and '1101100' to check if it returns '6C'. This step ensures the logic and conversion process have been correctly implemented.

Key concepts

Binary Number System

The Binary Number System is a fundamental concept in computing and digital electronics. It consists of only two digits: 0 and 1. Every number or computing task your computer performs is based on this simple system. Each digit in a binary number represents a power of 2, with the rightmost digit representing 2 raised to the power of 0.

• Binary number '1011' can be understood as:
• $$1\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0=11$$
• This is known as the binary-to-decimal conversion.

Binary is essential because it aligns with the binary state of digital components, which operate in on-off (1-0) states. Understanding this system lays the groundwork for more complex computing concepts.

Hexadecimal Number System

The Hexadecimal Number System is based on 16 digits, comprising numbers 0 to 9 and letters A to F, where A through F represent the additional six values. This system is a more human-friendly representation of binary-coded values and is frequently used in programming and data storage.

• Hexadecimal simplifies the reading and management of large binary numbers.
• It's compact: four binary digits can be represented by a single hexadecimal digit.

For instance, the binary '1101100' converts to the hexadecimal value '6C'. This conversion is crucial for debugging and reading memory addresses in programming. The notation for hexadecimal values usually begins with '0x' in many programming languages to indicate their base.

Programming Functions

In programming, functions are essential tools for breaking down tasks into manageable code blocks. They allow for reusability, modularity, and separation of concerns within your code.

• Functions take inputs, perform specified operations, and return outputs.
• They make the code more readable and maintainable.

The process of converting a binary number to hexadecimal, as provided in the exercise, is efficiently executed by defining a function. The function would accept a binary string as input, convert it to a decimal using a built-in function like `int()`, and then convert the result to hexadecimal using `hex()`. Such functions can be tested for correctness in different scenarios, ensuring reliability in the code.

Data Storage in Programming

Data storage is a critical aspect of programming, where the choice of storage method impacts efficiency and performance. After converting a binary number to hexadecimal, storing this information effectively ensures it's readily available when needed.

• Variables are used to store single values, like a converted hexadecimal.
• Data structures, such as arrays, lists, or dictionaries, help manage multiple values.
• Choosing appropriate storage is crucial based on the expected use.

In our exercise, once we've converted the binary to hex, we can store it in a single variable or within a data structure for managing larger datasets. Knowing where and how to store data ensures faster access and manipulation, which is essential for efficient program execution.