Digital Electronic Circuit

Question 1:  Convert 1012₁₀ base 8 using the weights in base 8.

Calculate 2031₁₀ in base 8 using the division conversion method.

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

 Question 3: Convert the following numbers from decimal to binary and then to hexadecimal (Don’t use IEEE 754 format for this question).

i) 31.875₁₀

ii) (4128.3125)₁₀

Question 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)

 Question 5: Represent 127.625 in a 32-bit IEEE 754 format