PLEASE SHOW MATH OF IT ALL

2. Given n bits, how many signed numbers can be represented using the sign-and-magnitude method, the ones complement method, and the twos complement method, respectively? (5 points)

3. Number conversion (2.5 x 22 = 55 points)

1. Convert the following unsigned binary numbers to decimal:

11111

101

2. Convert the following decimal numbers to binary:

111

35

3. Convert the following octal numbers to binary:

1111

731

4. Convert the following unsigned binary numbers to octal:

101010111001

1001

5. Convert the following decimal numbers to octal:

512

127

6. Convert the following octal numbers to decimal:

101

2345

7. Convert the following unsigned binary numbers to hexadecimal:

1010001001001111

1000110011111

8. Convert the following hexadecimal numbers to binary:

abcdef

3A2B

1. Convert the following decimal numbers to hexadecimal:

1111

13579

10. Convert the following hexadecimal numbers to decimal:

bdef

FACE

11. Convert the following numbers as required:

43₅ to base-3

2C5₁₆ to base-4

4. Fraction conversion (2.5 x 8 = 20 points)

1. 0.3125₁₀ to octal
2. 3.625₁₀ to binary
3. 2.0546875₁₀ to hexadecimal
4. 0.2EC5₁₆ to decimal
5. 0.1011₂ to decimal
6. 0.101101₂ to hexadecimal
7. 0.01011101₂ to octal
8. 3.572₈ to binary