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July 15, 2009 Page 1 of 7
Name:
Student Number:
- Check that your exam includes all 7 pages.
- PRINT your name and student number in the spaces above.
- Read all instructions and problems carefully. Points will be deducted for failure to follow instructions.
- Show ALL of your work on these pages. If you need extra space for a particular problem, write on the back of the previous page.
- You are NOT permitted to use notes, books, calculators, or other resources during this exam.
- This exam lasts for 100 minutes. Point values are listed for each problem to assist you in best using your time.
Problem 1. (24 points possible)
Problem 2. (12 points possible)
Problem 3. (20 points possible)
Problem 4. (14 points possible)
Problem 5. (14 points possible)
Problem 6. (16 points possible)
TOTAL. (100 points possible)
July 15, 2009 Page 2 of 7
Problem 1. (24 points)
A. (10 points) Each row in the table below lists a decimal value and its binary representation in both 6-bit sign-magnitude and 6-bit 2’s-complement representations. Complete the table, filling in the missing entries in each row.
Value (decimal)
6-bit sign-magnitude binary representation
6-bit 2’s-complement binary representation
29
0 1 0 1 1 1
1 1 1 0 1 0
1 1 0 1 1 0
B. (9 points) Perform each of the following additions using 6-bit 2’s-complement integer arithmetic. Write your answers in the boxes provided for each problem and circle the answers indicating the value of the carry-out bit and whether or not overflow occurred.
carry-out: 0 1 carry-out: 0 1 carry-out: 0 1 overflow: yes no overflow: yes no overflow: yes no
C. (5 points) Perform the following subtraction using 6-bit 2’s-complement integer arithmetic. Write your answer in the box provided and circle the answer indicating whether or not overflow occurred.
overflow: yes no overflow: yes no
July 15, 2009 Page 4 of 7
Problem 3. (20 points)
A sequence detector is defined by the state table to the right. This FSM has a single input, X, and a single output, Z.
A. (1 point) What type of FSM is this? (circle one) Moore Mealy
B. (4 points) In the space below, draw a state diagram for this FSM.
C. (12 points) This FSM will be implemented using D flip-flops. Complete the Karnaugh maps and derive minimal SOP or POS equations for the flip-flop inputs and the output.
D 1 =
D 0 =
Z =
D. (2 points) Assuming the FSM is initially in state A, what is the shortest input sequence detected (Z=1)?
E. (1 point) Are overlapped sequences detected by this FSM? Yes No
S 1 S 0 X S 1 +^ S 0 +^ Z
(A)
(B)
(C)
(D)
0 1 00
01
11 10
S 1 S 0
X
D 1
0 1 00 01
11 10
S 1 S 0
X
D 0
0 1 00 01
11 10
S 1 S 0
X
Z
July 15, 2009 Page 5 of 7
Problem 4. (14 points)
A finite state machine is to be designed that has two inputs, <X 1 X 0 >, and two outputs, <Z 1 Z 0 >, and that behaves according to the following rules:
- If X 1 = X 0 for two or more consecutive cycles, <Z 1 Z 0 > = <10>
- If X 1 = X 0 for two or more consecutive cycles, <Z 1 Z 0 > = <01>
- <Z 1 Z 0 > = <00> otherwise
In the spaces below, draw state diagrams for implementing this machine in both Moore and Mealy forms. You should attempt to minimize the number of states required.
A. (7 points) Moore machine key:
B. (7 points) Mealy machine key:
S
X 1 X 0 / Z 1 Z 0
X 1 X 0
S
Z 1 Z 0
July 15, 2009 Page 7 of 7
Problem 6. (16 points)
A new device, which will be called a priority multiplexer, is to be designed. The truth table and schematic symbol for this device are shown below.
A. (6 points) Write algebraic expressions for the outputs F and VALID. It is NOT necessary to derive minimal expressions.
F =
VALID =
B. (10 points) Draw the schematic for a circuit implementing this function using logic gates (INVERTERs, ANDs, ORs, NANDs, NORs), transmission gates (pass transistors), or a combination of these. You should make a reasonable effort to produce an efficient design, although this will not be a major factor in grading.
EN A B C VALID F
0 x x x 0 x
1 1 x x 1 IA
1 0 1 x 1 IB
1 0 0 1 1 IC
1 0 0 0 0 x
IA IB IC
EN
A B C
F
VALID
