Convert the numbers from decimal to binary and then to

Question

Homework

1. Convert 1012₁₀ into base 8 using the weights in base 8. And calculate 2031₁₀ in base 8 using the division conversion method.

2. Suppose you have a number 110001010100₂, can you directly change it from binary to hexadecimal. List the mapping from binary to hexadecimal.

3. Convert the following numbers from decimal to binary and then to hexiadecimal (Don't use IEEE 754 format for this question)
31.875
4128.3125

4. Explain how multiplication was implemented in binary format in computers. Use an example such as 156*25 to explain the multiplication step by step. (Here you need to show the detailed steps of binary multiplication)

5. Represent 127.625 in a 32-bit IEEE 754 format