note in a you should use 0 and 1 for completing the truth table

Task 2: How many days? In a digital calendar (for example, in a wristwatch) an important function is to relate the month to the number of days in the month. Given the inputs DCBA to represent the month, where 0001 is January and 1100 is December, the truth table below represents three output variables X,Y,Z corresponding to having 28 days, 30 days or 31 days respectively. X has been completed for you. Note: invalid inputs such as 0000 result in 000 output, and leap years are not considered. a. Complete the truth table for Y and Z. b. Draw the Karnaugh maps for Y and Z and find the simplified Boolean algebra expressions for Y and Z. Show the groups obtained and explain your working. c. Any circuit can be represented using NOR gates only. Do this for Y. First apply Boolean algebra to convert the sum-of-products expression obtained in part b into a product-of-sums expression. De Morgan's law will help you here. Second, take the product-of-sums expression of part c and push the NOT bubbles through to create a NOR circuit. Draw it. d. Demonstrate your NOR-gate-only circuit is correct by drawing the truth table. Your table should have the general form shown below: D, C, B, A are the original inputs and column number 1 is the column for Y taken from the table created in part a. Columns 2, 3,... represent the sub-expressions of our NOR representation. You decide how many you need based on the expressions. The last columa n is the final NOR representation of Y. Clearly, it should match column 1. If it does not, don't panic: you will get credit for carrect working. Hint: Using a spreadsheet program such as Excel is a comvenient way of building a truth table