100112 +101102

1011012 +1101112

2. Complete the Full-Adder truth table for the sum (s_i) and carry-out (c_i+1) functions.

xi	yi	carry-in ci	sum si	carry-out ci+1
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

3. Use k-maps to minimize the sum (s_i) and carry-out (c_i+1) functions of the Full-Adder:

4. For the one-bit Full-Adder, how many gate delays are needed before the carry-out (c_i+1) wire is correct?

5. A 32-bit, ripple-adder is made up of a collection of single-bit Full-Adders connected together as shown below:

How many gate delays are needed before c₃₂ is correct?

6. To speed up the calculation of the carry-out (C_i+1) signals, consider constructing a 32-bit adder using two-bit adders as shown in:

If c_i+1 is calculated directly from the inputs as c _i+1 = x_i y_i + x_i x_i-1 y_i-1 + x_i x_i-1 c_i-1 + x_i y_i-1 c_i-1

+ y_i x_i-1 y_i-1 + y_i x_i-1 c_i-1 + y_i y_i-1 c_i-1, then how many gate delays would be needed to calculate the c_i+1 signal in a two-bit adder?

7. What would be the total number of gate delays in a 32-bit adder before the c ₃₂ signal is generated correctly if two-bit adders were used?

8. a) If R = 0 and S = 1, then what will be the output on Q and ?

b) Now, if S goes to a 0 value, what happens to the output on Q and ?