Convert 2's Complement to Hexadecimal: Step-by-Step

SenseBridge

2 min read

·

25-10-2024

1

0

Share

Converting a 2's complement binary number to hexadecimal can be a straightforward process if you follow the right steps. In this guide, we will walk through the steps needed to convert a 2's complement binary representation into its hexadecimal equivalent, illustrating the process with examples to make it easier to understand. Let's get started! 📘

Understanding 2's Complement

Before we dive into the conversion process, it’s essential to grasp what 2's complement is. 2's complement is a method for representing signed integers in binary. The most significant bit (MSB) indicates the sign of the number: if it is 0, the number is positive, and if it is 1, the number is negative. The range for an n-bit number in 2's complement is from -2^(n-1) to 2^(n-1)-1.

Key Points to Remember:

• MSB = 0 → Positive number
• MSB = 1 → Negative number
• In 8 bits, the range is from -128 to +127.

Step-by-Step Conversion Process

Let's break down the conversion process into manageable steps. We will convert a binary number in 2's complement to its hexadecimal form.

Step 1: Identify the Bit Length

Determine the number of bits in the binary number. For instance, if you have an 8-bit binary number like 11111100, you will proceed with the conversion knowing it is an 8-bit number.

Step 2: Check the Sign Bit

Check the most significant bit (the leftmost bit):

• If it's 0, the number is positive, and you can directly convert it to hexadecimal.
• If it's 1, the number is negative, and you'll need to convert it to its positive equivalent first.

Example 1: Positive Number Conversion

Let’s take a positive 2's complement binary number: 01100101 (which represents +101 in decimal).

Conversion Steps:

1. Convert Binary to Decimal:

   • 01100101 = 0*2^7 + 1*2^6 + 1*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 0*2^1 + 1*2^0
   • = 0 + 64 + 32 + 0 + 0 + 4 + 0 + 1 = 101

2. Convert Decimal to Hexadecimal:

   • 101 in decimal = 65 in hexadecimal.

Hexadecimal Result: 65

Example 2: Negative Number Conversion

Now, let’s consider a negative 2's complement binary number: 11111010 (which represents -6 in decimal).

Conversion Steps:

1. Find the Positive Equivalent:

   • To find the positive value, first, take the 2's complement:
     • Invert the digits: 00000101
     • Add 1: 00000101 + 1 = 00000110 (which is 6 in decimal).

2. Convert to Hexadecimal:

   • 6 in decimal = 06 in hexadecimal.

Hexadecimal Result: 06

Step 3: Group the Binary into Nibbles

If you have a longer binary number (e.g., 16 bits), divide it into nibbles (groups of 4 bits). Each nibble corresponds to a single hexadecimal digit.

Example 3: 16-bit Conversion

Consider the 16-bit binary number 1111111100000001.

1. Grouping into Nibbles:

   1111 1110 0000 0001
   

2. Convert Each Nibble to Hexadecimal:

   • 1111 = F
   • 1110 = E
   • 0000 = 0
   • 0001 = 1

Hexadecimal Result: FE01

Conversion Table

For your convenience, here’s a simple conversion table of binary to hexadecimal:

Important Notes

Remember: Always check the sign bit before converting negative numbers. The two's complement method allows us to efficiently represent negative integers.

Conclusion

By following these steps, converting a 2's complement binary number to its hexadecimal representation becomes an easy task. This process can be particularly useful in programming and digital design where both binary and hexadecimal representations are frequently used. Make sure to practice with both positive and negative numbers to become proficient in these conversions! Happy converting! 🎉