What Is Two's Complement and How to Use It for Addition?

TL;DR

Two's complement allows for addition and subtraction by converting subtraction into addition problems. To find a negative number's two's complement, flip all the bits and add one. Overflow occurs when adding two positive or two negative numbers leads to a result with the opposite sign, indicating the result exceeded the available bit range.

Transcript

The nice feature of two's complement representation is that it allows you to do both addition and subtraction as addition problems, by simply turning the subtraction problem A-B into an addition problem of A + (-B). Since we now know how to easily negate values in two's complement, this is pretty straight forward. For example, let's perform 15 - 18... Read More

Key Insights

• ❓ Two's complement representation simplifies addition and subtraction by treating subtraction problems as addition problems.
• 🫦 Negative numbers in two's complement are obtained by flipping all the bits of the positive representation and adding one.
• 🔢 Overflow in two's complement addition can be detected by comparing the signs of the input numbers and the resulting number.

Questions & Answers

Q: How does two's complement representation simplify subtraction?

Two's complement allows subtraction problems to be solved as addition problems by simply adding the negative value. This eliminates the need for separate subtraction algorithms.

Q: How is a negative number represented in the two's complement form?

To represent a negative number in two's complement, flip all the bits of the positive representation and add one to the result. This yields the equivalent negative value.

Q: How is overflow detected in two's complement addition?

Overflow in two's complement addition can be detected by comparing the signs of the two numbers being added and the sign of the resulting number. If the signs do not match, overflow has occurred.

Q: Can overflow occur when adding a positive and negative number?

No, overflow cannot occur when adding a positive and negative number within the range of representable values. Overflow only occurs when adding two numbers of the same sign.

Summary & Key Takeaways

• Two's complement representation allows for addition and subtraction by converting subtraction problems into addition problems.

• To convert a negative number to its two's complement representation, flip all the bits and add one.

• Overflow can occur when adding two positive numbers and the result is negative, or when adding two negative numbers and the result is positive.