What is the largest positive number one can represent in 5-bit 2’s complement code?

In 5-bit 2's complement representation, the most significant bit (MSB) is the sign bit. It indicates whether the number is positive (0) or negative (1). The remaining 4 bits represent the magnitude of the number.

### Steps:
- The smallest number (most negative) in 5-bit 2's complement is represented by `10000`, which equals -16.
- The largest number (most positive) is represented by `01111`.

For a 5-bit 2's complement number:
- The binary representation of the largest positive number is `01111`.
- This is \(0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\).

Calculating the decimal value:
\[
2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1 = 15
\]

Thus, the largest positive number that can be represented in 5-bit 2's complement is **15**.

Would you like more details or have any questions?

Here are 5 related questions for you:
1. How do you represent the smallest negative number in 5-bit 2's complement?
2. What is the range of numbers that can be represented in a 6-bit 2's complement system?
3. How does 2’s complement simplify the process of subtraction in binary?
4. Can you explain how to convert a negative decimal number to 2’s complement?
5. What happens if you try to represent a number larger than the 2's complement range?

**Tip**: When converting a negative number into 2's complement, flip all the bits and add 1!

Explore the 5-bit 2’s complement representation system and learn how to determine the largest positive number. This guide covers essential concepts such as binary numbers, 2’s complement representation, and bitwise operations. Perfect for students in Grades 9-12.

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