1. In the following, A, B, and C are Boolean variables, fill in the following with your simplest (minimum number of literals) answers. ' Denotes the complement of the variable. A is the complement of A.

1. (1 Point Each)

1. A +A = _______

2. A + 1 = ____

3. X + X = ____

4. A. A' = ___

(II) (2 Points Each)

1. A.B + A. C = _____________________________

2. A.B + A.B' = _____________________________

3. A. (A' + B) = _____________________________

2. (5 Points) Draw the logic diagram for the following function using NOT, AND, and OR gates.

F (A, B) = A. B + A.B'+A'. B' + A'. B

3. (5 Points) Simplify the following Boolean functions. Show your work.

F (A, B) = A. B + A.B'+A'. B' + A'. B

CS 221 QNO Logic Design Page 2

Problem # 2 [20 Points]

Assume for the following questions that the register is 6-bit long. Specify all zeros of the system.

1. How many different numbers can be represented on this 6-bit register? ______

2. What is the smallest value of the unsigned integer on this 6-bit register? ______

3. What is the largest value of the unsigned integer on this 6-bit register? ______

4. Write down the values of the integers represented by binary values in the specified representation

A	B	C	D	E	F	Number in Sign-Magnitude Form	Number in 1s Complement	Number in 2 Complement
0	1	1	1	1	1
1	0	0	0	0	0
1	0	0	0	0	1
1	0	0	0	1	0
1	1	1	1	1	0
1	1	1	1	1	1

5. What is the 2s complement of the binary integer 111111? ____________

6. What is the 1s complement of the binary integer 111111? ____________

7. What is the presentation of decimal integer -20 on a 6-bit register using 2 complements? Show your work? ___________

CS 221 QNO Logic Design Page 3

Problem # 3 [14 Points]

1. Add the two pairs of binary numbers X = 00101 and Y = 10111and show the results in binary. (Be sure to show the carry as you add.) Let us the call the result Z = X +Y.

Carries

0 0 1 0 1 (X)

+ 1 0 1 1 1 (Y)

(Z)

2. Convert the binary integer 1010101011 to decimal. ____________

3. Convert decimal integer 1393 to binary. Show all your work, quotients, and remainders, and then write down the answer. _____________________

4. Convert decimal integer 1393 to hexadecimal. You can use the answer from part (C) or could use calculator to do division. Show you work either way.