1. ECE 434 Advanced Digital System L13
Electrical and Computer Engineering University of Western Ontario

2. Review: Block Diagram of a Binary Multiplier
Ad – add signal // adder outputs are stored into the ACC
Sh – shift signal // shift all 9 bits to right
Ld – load signal // load multiplier into the 4 lower bits of the ACC and clear the upper 5 bits
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3. Review: State Graph for Binary Multiplier
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4. Review: Multiplier Control with Counter (cont’d)
Increment counter each time a shift signal is generated
Generate K after n-1 shifts occured
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5. Review: Array Multiplier
What do we need to realize Array Multiplier?
AND gates = ?
FA = ?
HA = ?
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6. Review: Array Multiplier (cont’d)
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7. Review: Multiplication of Signed Binary Numbers
How to multiply signed binary numbers?
Procedure
Complement the multiplier if negative
Complement the multiplicand if negative
Multiply two positive binary numbers
Complement the product if it should be negative
Simple but requires more hardware and time than other available methods
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8. Review: Multiplication of Signed Binary Numbers
Four cases
Multiplicand is positive, multiplier is positive
Multiplicand is negative, multiplier is positive
Multiplicand is positive, multiplier is negative
Multiplier is negative, multiplicand is negative
Examples
0111 x 0101 = ?
1101 x 0101 = ?
0101 x 1101 = ?
1011 x 1101 = ?
Preserve the sign of the partial product at each step
If multiplier is negative, complement the multiplicand before adding it in at the last step
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9. Review: 2’s Complement Multiplier
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10. State Graph for 2’s Complement Multiplier
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11. Faster Multiplier
Move wires from the adder outputs one position to the right => add and shift can occur at the same clock cycle
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12. State Graph for Faster Multiplier
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13. Behavioral Model for Faster Multiplier
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14. Behavioral Model for Faster Multiplier
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15. Command File and Simulation
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16. Test Bench for Signed Multiplier
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17. Digital design with SM Charts
State graphs used to describe state machines controlling a digital system
Alternative: use state machine flowchart
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18. State Machine Charts SM chart or ASM (Algorithmic State Machine) chart
Easier to understand the operation of digital system by examining of the SM chart instead of equivalent state graph
SM chart leads directly to hardware realization
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19. Components of SM charts
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20. SM chart is constructed from SM blocks
State S1 is entered =>
Z1 and Z2 become 1
if X1=0 Z3 and Z4 become 1
if X1=1 and X3=0 Z5 become 1
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21. Equivalent SM Blocks
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22. Equivalent SM Charts for Comb Networks
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23. Block with Feedback
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24. Equivalent SM Blocks
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25. Converting a State Graph to an SM Chart
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26. Derivation of SM Charts
Binary Multiplier
Dice Game
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27. SM Chart for Binary Multiplier
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28. VHDL for Multiplier SM Chart (I)
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29. VHDL for Multiplier SM Chart (II)
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30. Electronic Dice Game Block diagram
1. Two counters simulate the roll of dice (1-6); sum of two counters is in range of 2-12
2. Reset – initiate new game
3. Rb – roll button; when the roll button is pressed the counters count at high speed; when the button is released, the values of counters are displayed and game can proceed.
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31. Electronic Dice Game - Description
First roll
player wins if the sum is 7 or 11
player loses if the sum is 2, 3 or 12
otherwise, the sum obtained in the first roll is referred as a point, and player must roll the dice again
Second roll (or subsequent roll)
player wins if the sum equals the point
player loses if the sum is 7
otherwise, player rolls again until she/he finally wins or loses
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32. Flowchart for Dice Game
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33. Control Network for Dice Game
Input signals to the control network
D7 – 1 if the sum of the dice is 1
D711 – (7 or 11)
D2312 – (2, 3, 12)
Eq – 1 if the sum equals the number stored in the point register
Rb – 1 when the roll button is pressed
Reset – 1 when the reset button is pressed
Output from the control network
Roll=1 – enables the dice counters
Sp=1 – sum is stored in the point register
Win=1 – turns on win light
Lose=1 – turns on lose light
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34. SM Chart for Dice Game
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35. State Graph for Dice Game
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36. Behavioral Model for Dice Game (1)
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37. Behavioral Model for Dice Game (2)
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38. To Do
Read chapters 4.1, 4.2, 4.3
Do homework #4
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