The Hexadecimal Number $4A_{16}$ Converts To What Binary Number?Select One: A. 10100100 $_{2}$ B. 01011011 $_{2}$ C. $01001010_{2}$ D. 10110101 $_{2}$
Introduction
In the world of computer programming and technology, numbers are represented in various forms, including hexadecimal and binary. Hexadecimal is a base-16 number system that uses 16 distinct symbols: 0-9 and A-F. Binary, on the other hand, is a base-2 number system that uses only two symbols: 0 and 1. In this article, we will explore the process of converting a hexadecimal number to its equivalent binary representation.
Understanding Hexadecimal Numbers
Before we dive into the conversion process, let's take a closer look at hexadecimal numbers. A hexadecimal number is represented by a series of digits, each of which can range from 0 to 9 or A to F. The subscript 16 indicates that the number is in base-16. For example, the hexadecimal number $4A_{16}$ consists of two digits: 4 and A.
The Conversion Process
To convert a hexadecimal number to its equivalent binary representation, we need to understand the relationship between the two number systems. In hexadecimal, each digit can represent 4 bits (2^2). To convert a hexadecimal number to binary, we need to multiply each digit by 16 (2^4) and then convert the result to binary.
Step 1: Multiply Each Digit by 16
Let's apply this process to the hexadecimal number $4A_{16}$. We will multiply each digit by 16 and then convert the result to binary.
- For the digit 4, we multiply it by 16: 4 × 16 = 64
- For the digit A, we multiply it by 16: A × 16 = 160
Step 2: Convert the Results to Binary
Now that we have the results of multiplying each digit by 16, we need to convert them to binary. To do this, we will divide each result by 2 and record the remainder.
- For the result 64, we divide it by 2: 64 ÷ 2 = 32 remainder 0
- For the result 32, we divide it by 2: 32 ÷ 2 = 16 remainder 0
- For the result 16, we divide it by 2: 16 ÷ 2 = 8 remainder 0
- For the result 8, we divide it by 2: 8 ÷ 2 = 4 remainder 0
- For the result 4, we divide it by 2: 4 ÷ 2 = 2 remainder 0
- For the result 2, we divide it by 2: 2 ÷ 2 = 1 remainder 0
- For the result 1, we divide it by 2: 1 ÷ 2 = 0 remainder 1
Step 3: Combine the Binary Results
Now that we have the binary representations of each result, we can combine them to form the final binary number.
- The binary representation of 64 is 1000000
- The binary representation of 160 is 10100000
The Final Binary Number
By combining the binary representations of each result, we get the final binary number: 10100000 1000000.
Conclusion
In this article, we explored the process of converting a hexadecimal number to its equivalent binary representation. We applied the conversion process to the hexadecimal number $4A_{16}$ and obtained the final binary number: 10100000 1000000. This process is essential in computer programming and technology, where numbers are represented in various forms.
The Answer
Introduction
In our previous article, we explored the process of converting a hexadecimal number to its equivalent binary representation. In this article, we will answer some frequently asked questions about hexadecimal to binary conversion.
Q: What is the difference between hexadecimal and binary?
A: Hexadecimal is a base-16 number system that uses 16 distinct symbols: 0-9 and A-F. Binary, on the other hand, is a base-2 number system that uses only two symbols: 0 and 1.
Q: Why do we need to convert hexadecimal to binary?
A: In computer programming and technology, numbers are represented in various forms. Hexadecimal is often used to represent large numbers, while binary is used to represent the actual values stored in computer memory. Converting hexadecimal to binary is essential for understanding how computer systems work.
Q: How do I convert a hexadecimal number to binary?
A: To convert a hexadecimal number to binary, you need to multiply each digit by 16 (2^4) and then convert the result to binary. You can use the following steps:
- Multiply each digit by 16
- Convert the results to binary
- Combine the binary results to form the final binary number
Q: What if I have a hexadecimal number with a letter (A-F)?
A: When you have a hexadecimal number with a letter (A-F), you need to convert it to its decimal equivalent first. For example, the hexadecimal number A is equivalent to 10 in decimal.
Q: Can I use a calculator to convert hexadecimal to binary?
A: Yes, you can use a calculator to convert hexadecimal to binary. Most calculators have a built-in function to convert hexadecimal to binary.
Q: How do I convert a binary number to hexadecimal?
A: To convert a binary number to hexadecimal, you need to divide the binary number by 16 (2^4) and record the remainder. You can use the following steps:
- Divide the binary number by 16
- Record the remainder
- Repeat the process until you get a remainder of 0
- Combine the remainders to form the final hexadecimal number
Q: What if I have a binary number with a 1 followed by zeros?
A: When you have a binary number with a 1 followed by zeros, you can ignore the zeros and only consider the 1. For example, the binary number 1000000 is equivalent to 64 in decimal.
Q: Can I use a programming language to convert hexadecimal to binary?
A: Yes, you can use a programming language to convert hexadecimal to binary. Most programming languages have built-in functions to convert hexadecimal to binary.
Conclusion
In this article, we answered some frequently asked questions about hexadecimal to binary conversion. We hope that this Q&A guide has helped you understand the process of converting hexadecimal to binary and how to use it in computer programming and technology.
Common Mistakes to Avoid
- Not understanding the difference between hexadecimal and binary
- Not following the correct conversion process
- Not considering the decimal equivalent of hexadecimal letters
- Not using a calculator or programming language to convert hexadecimal to binary
Best Practices
- Always follow the correct conversion process
- Use a calculator or programming language to convert hexadecimal to binary
- Consider the decimal equivalent of hexadecimal letters
- Practice converting hexadecimal to binary to improve your skills