What Is The First Step In Converting A Negative Decimal Number To Two's Complement?A. Convert To Binary B. Flip All Bits C. Add 1 D. Convert To Octal

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In the world of computer science, binary numbers are the foundation of digital information processing. However, not all binary numbers are created equal. Negative numbers, in particular, require a special representation to ensure accurate calculations. This is where two's complement comes in – a method of representing signed binary numbers using a combination of positive and negative values. In this article, we will delve into the first step of converting a negative decimal number to two's complement.

What is Two's Complement?

Two's complement is a way of representing signed binary numbers using a combination of positive and negative values. It is called "two's complement" because it involves adding 1 to the binary representation of a negative number. This method is widely used in computer arithmetic, as it allows for efficient and accurate calculations.

Why is Two's Complement Important?

Two's complement is essential in computer science because it enables the representation of signed binary numbers in a way that is easy to work with. It allows for efficient addition and subtraction operations, which are critical in many applications, such as arithmetic, logic, and control.

Converting a Negative Decimal Number to Two's Complement

Now that we have a basic understanding of two's complement, let's dive into the first step of converting a negative decimal number to two's complement.

Step 1: Convert to Binary

The first step in converting a negative decimal number to two's complement is to convert the decimal number to its binary representation. This involves dividing the decimal number by 2 and keeping track of the remainders until the quotient is 0.

Example: Converting -5 to Binary

To convert -5 to binary, we can follow these steps:

  1. Divide -5 by 2: -5 ÷ 2 = -2 remainder -1
  2. Divide -2 by 2: -2 ÷ 2 = -1 remainder -0
  3. Divide -1 by 2: -1 ÷ 2 = 0 remainder -1

The binary representation of -5 is therefore 1111.

Step 2: Flip All Bits

Once we have the binary representation of the negative decimal number, the next step is to flip all the bits. This involves changing each 0 to a 1 and each 1 to a 0.

Example: Flipping the Bits of 1111

To flip the bits of 1111, we can simply change each 1 to a 0 and each 0 to a 1. The resulting binary number is 0000.

Step 3: Add 1

The final step in converting a negative decimal number to two's complement is to add 1 to the binary number obtained in the previous step.

Example: Adding 1 to 0000

To add 1 to 0000, we can simply append a 1 to the end of the binary number. The resulting binary number is 0001.

Conclusion

In conclusion, the first step in converting a negative decimal number to two's complement is to convert the decimal number to its binary representation. This involves dividing the decimal number by 2 and keeping track of the remainders until the quotient is 0. The binary representation of the negative decimal number is then flipped, and finally, 1 is added to the resulting binary number.

Key Takeaways

  • Two's complement is a method of representing signed binary numbers using a combination of positive and negative values.
  • The first step in converting a negative decimal number to two's complement is to convert the decimal number to its binary representation.
  • The binary representation of the negative decimal number is then flipped, and finally, 1 is added to the resulting binary number.

Frequently Asked Questions

Q: What is two's complement?

A: Two's complement is a method of representing signed binary numbers using a combination of positive and negative values.

Q: Why is two's complement important?

A: Two's complement is essential in computer science because it enables the representation of signed binary numbers in a way that is easy to work with.

Q: How do I convert a negative decimal number to two's complement?

A: To convert a negative decimal number to two's complement, you need to follow these steps:

  1. Convert the decimal number to its binary representation.
  2. Flip all the bits of the binary number.
  3. Add 1 to the resulting binary number.

References

  • [1] "Two's Complement" by Wikipedia
  • [2] "Binary Numbers" by Khan Academy
  • [3] "Two's Complement Representation" by GeeksforGeeks

Related Topics

  • Binary Numbers
  • Two's Complement Representation
  • Signed Binary Numbers
  • Computer Arithmetic
  • Logic and Control