I know this shows the solution, but I would still like an explanation so I can understand exactly what is happening and the main point of the question, thank you! Please explain the solution using your own notes/words ^_^

3 [20 pts] Floating point numbers [10 pts] Convert 12.8125 into single precision floating point Binary representation using IEEE 754 standard. Write your answer in both Binary and Hex formats. Show your work for partial credit. a. 0100 0001 0100 1101 0000 0000 0000 0000 0x414d0000 Steps: 1100.1101 1.1001101 x 2A3 Exponent- 130 or 1000 0010 Mantissa 100 1101 0000 0000 0000 0000 b. [10 pts] Convert the following single precision floating point Hex representation into decimal number using IEEE 754 standard. Show your work for partial credit. 0x41AA0000 21.25 Steps: 0100 0001 1010 1010 0000 0000 0000 0000 sign 0 exp 10000011- 131-4 mantissa 010 1010 0000 0000 0000 0000 1.010101 x 2A4 10101.01 16+4+1+0.25 21.25