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!