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March 28, 2001 Page 1 of 5
Name:
Student Number:
- Check that your exam includes all 5 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 75 minutes. Point values are listed for each problem to assist you in best using your time.
Problem 1. (20 points possible)
Problem 2. ( 9 points possible)
Problem 3. (11 points possible)
Problem 4. (10 points possible)
TOTAL. (50 points possible)
February 7, 2001 Page 2 of 5
Problem 1. (20 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 formats. 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
23
1 0 1 0 1 0
0 1 1 0 1 0
1 1 0 1 1 0
B. (6 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. (4 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
February 7, 2001 Page 4 of 5
Problem 3. (11 points)
A. (5 points) A circuit is to be designed that generates a single “1” each time it detects the sequence “110.” This sequential circuit has one input, X, and one output, Z. Complete the state diagram below, labeling the outputs for the transition arcs already shown and adding and labeling any additional states and/or transitions arcs needed. You should attempt to minimize the number of states used. Assume that state A is the initial state.
X/Z
S
key:
A B C
B. (6 points) A two-phase clocked register (flip-flop) is to be designed. This register has two clock inputs (phi1, phi2), two control inputs (LOAD, INV), one data input (D), and one output (Q). The logical behavior of this register is described by the truth table at the right. (Q
is the next state of the register.)
LOAD INV Q+ 0 0 Q 0 1 Q 1 0 D 1 1 D The register is to be designed using two clocked latches (already drawn below) and some combination of INVERTERs, 2-input NANDs, and 2-input XORs. (You are not required to use all of these gate types and you may use as many of each type as you choose.) Complete the schematic below for this circuit, clearly labeling all of the inputs and the output. You should make a reasonable effort to minimize circuit complexity.
phi
IN OUT
CLK
phi
IN OUT
CLK
February 7, 2001 Page 5 of 5
Problem 4. (10 points)
A. A 3-bit counter (whose outputs are labeled Q3, Q2, and Q1) is to be designed to count in a Gray Code sequence, as follows:
Q3Q2Q1: 000 –> 001 –> 101 –> 100 –> 110 –> 111 –> 011 –> 010 –> 000 –> …
The two inputs to this circuit, aside from the clocks, are Count Enable (CE) and Clear (CLR). You may implement this circuit using either D register cells or toggle register cells (1-bit counters) as the basic building block. (Check the appropriate line below to indicate your choice.) Draw the schematic for your circuit. It is not necessary to show the internal circuitry of your registers (just draw their symbols) or the clock lines. You may use any of the basic logic gates to implement the remaining circuitry. You MUST provide sufficient work to clearly show how you derived your circuit.
_____ D register _____ toggle register (1-bit counter)
D Q Clear
CE Out Clear
