Hint for 13-25
Work out the sixteen rows of the truth table and construct the Karnaugh map. There should only be three zeroes.
Ignore the answer in the back of the text!
Hint for 13-30
Boxing the ones yields an expression involving just three gates when the x is taken as 1. However, when the zeroes are boxed and the result NOTted, as shown in the class example, followed by several applications of DeMorgans' theorems, you can find an expression using just two gates that will yield the desired truth table.
Hint for 13-35
First make a circuit that adds one bit from the number A and a corresponding bit from number B. After the circuit module for adding corresponding bits is available, an adder for four bits may be assembled from four such single-bit adder modules.
Don't forget that a carry bit input, name it Ci should be included to incorporate overflow from the preceding addition of lower-significance bits.
Also note that you will need two output bits, one for the sum bit S and the other for the carry bit output Co.
Hint for S13.1
Refer to your notes from our recent class and model after the proof of DeMorgan's first theorem that was presented.
Hint for S13.2
Refer to your class notes on our discussion of segment a. Also, warm up on the Karnaugh map started for the simpler gate combination for segment c.