Question 1: Convert the following decimal numbers to binary and hexadecimal: 37, 333, 65537

Question 2: Convert the following signed 8-bit binary numbers to two's complement: -00000001, -00110011, -01010101

Question 3: Perform the following three subtraction operations by converting the numbers to 8-bit two's complement and adding: 65-32, 32-65, 16-10

Recall algorithms discussed during lecture for computing the two's complement of a negative number:

Algorithm #1:

1.Copy down the digits starting from the right

2.Proceed left until the first 1 bit has been copied

3.After copying the first one, copy down the complement of the remaining bits

Algorithm #2:

Complement the number (switch all 0's to 1's and 1's to 0's)

Add 1

Question 4: Draw a logic circuit for (A B) (C D) C

Question 5: A bulb in a stairway has two switches, one switch being at the first floor and the other one at the second floor. The bulb can be turned ON and OFF by one of the switches regardless of the state of the other switch. What logic gate resembles the logic of switching of the bulb? Using the truth table for this behavior can help. Show your work!