Two's Complement in Action: Binary Arithmetic

Why Do Computers Add to Subtract?

You've learned how to represent negative numbers using two's complement. Now, let's explore the reason why it's so powerful. Two's complement allows a computer's processor to use the exact same circuits for addition and subtraction!

This quiz focuses on the practical application of two's complement in binary arithmetic. Understanding this is crucial for Computer Science, as it explains how computers perform calculations efficiently at the lowest level.

Get Ready to Calculate in Binary!

How Binary Arithmetic Works

Before you start, review these examples. They demonstrate how two's complement allows us to solve any addition or subtraction problem with simple binary addition.

Worked Example: Adding a Positive and Negative Number

Let's calculate 25 + (-10) using 8-bit two's complement. The answer should be 15.

  1. Step 1: Convert both numbers to 8-bit two's complement.
    - Positive 25 is simply 00011001.
    - For negative -10, we convert 10 to binary (00001010), invert (11110101), and add 1, which gives 11110110.
  2. Step 2: Add the binary numbers together.
    Add them just like regular column addition.
    00011001 (25) + 11110110 (-10) ------------------ 1 00001111
  3. Step 3: Handle the result.
    The addition resulted in 9 bits. In an 8-bit system, we discard the final carry bit (the leftmost '1').
    The remaining 8-bit result is 00001111.
  4. Step 4: Convert back to decimal to check.
    The binary 00001111 converts to the decimal number 15. It worked!
Question 1 of 10

Scenario: You are designing a simple Arithmetic Logic Unit (ALU). Ensure your understanding of two's complement arithmetic is perfect to prevent calculation errors in the hardware.

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