1. Elec 2607 Digital Switching Circuits
Lecture 21 & 22: Digital Logic
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2. This is infinitely more fun than factoring and multiplying out
Exam April 9 AM
This is infinitely more fun than factoring and multiplying out
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3. ANOTHER FORM OF Digital Logic
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4. Next slide
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5. 17/01/2019
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6. Next slide
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7. Were the literal count comes from
This slide
Were the literal count comes from
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8. Next slide
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9. Counting the Gate inputs
This slide
Counting the Gate inputs
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10. Next slide
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11. Where the gate count comes from
This slide
Where the gate count comes from
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12. 8
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13. Next slide
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14. Next slide
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15. Next slide
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16. Next slide
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17. Were the literal count comes from
This slide 11
Were the literal count comes from 3 3
vwu
vwu 6 6
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18. Next slide
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19. Counting the Gate inputs
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Counting the Gate inputs 11 5 5 6 6
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20. Next slide
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21. Where the gate count comes from
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Where the gate count comes from 1 1 2
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22. 1
Think about this
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23. Solution to 5.8 1 1 1 1 1 1 F E What about the don’t cares????
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24. 1 1 d 1 1 1 d d 1 d 1 1 F E
Treat as zero or 1: Use to make loops larger!!!!
Solution to 5.8
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25. Solution to 5.8 1 1 d 1 1 1 d d 1 d 1 1 F E 17/01/2019 17/01/2019
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26. Solution to 5.8 1 1 1 d 1 1 d d 1 d 1 1 F E XZ’ Shared gates 2 XY
Total gates required 5
F = AND AND
WX’
2 + 1 = 3
E = AND AND AND
= 4
Solution to 5.8
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27. W X Y Z
E F
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28. 17/01/2019
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29. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
gate solution
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30. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
gate solution
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31. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
gate solution
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32. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
gate solution
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33. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
E done
gate solution
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34. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
E done
gate solution
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35. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
E done
gate solution
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36. Find 1’s that have no other option and can share
All 1’s are common
Find 1’s that have no other option and can share
E done
F done
G done
gate solution
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37. Need 3 collecting OR Gates
E done
F done
G done
7 AND Terms
Need 3 collecting OR Gates
gate solution
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38. A B C D E F G F E
extra G
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39. Need 3 collecting OR Gates 5 AND Terms 5.9 9 gate solution
E done
F done
G done
1 XOR
Need 3 collecting OR Gates
5 AND Terms
gate solution
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40. 5.9 Find the other 9 gate solution that does not use the exclusive or.
E done
F done
G done
5.9 Find the other 9 gate solution that does not use the exclusive or.
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42. Not an error
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45. The 4 maps on the same page
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56. = 6
= 9
= 5
= 4
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57. NOTE ON GATE COUNT
In the expressions, a single input such as b as an AND term does not require and AND Gate. It is directly fed as input into the all collecting OR Gate.
= 3
= 5
= 3
= 3
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58. NOTE ON GATE COUNT
In the expressions, a single input such as b as an AND term does not require and AND Gate. It is directly fed as input into the all collecting OR Gate.
AND = 9
OR = 4
AND = 4
OR = 4
= 8
= 13
AND = 4
OR = 3
AND = 4
OR = 2
= 7
= 6
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59. 17/01/2019
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60. Another AND gate needed for remaining “UN-LOOPED” 1
If this 1 can be shared then it may not increase the gate count and then W would only need one unique AND gate and one AND gate shared from another MAP.
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62. E done F done G done Loop is not a gate
5.9 Found the other 9 gate solution that does not use the exclusive or.
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63. On A PAL single input cost one gate
A B C D E F G F E
On A PAL single input cost one gate
extra G
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64. Read
And
Remember
R&R
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87. With 1101 used for decimal point
Extra gate. In the wording of 5.10 this remaining 1 may have been overlooked.
Try to resolve the problem using a different set of maps. See if you can obtain the same number of gates and only two additional gate inputs.
5.10
With 1101 used for decimal point
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89. A GOOD PLACE TO TAKE A BREAK
A GOOD PLACE TO START AGAIN
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93. 7-loop 2 brother with friends 8-loop 2 brother with friends
5.12
4- loop 4 no friends
7-loop 2 brother with friends
8-loop 2 brother with friends
3-loop 2 friends are gone
5-loop 4 with no friends
7-loop 2 brother with friends
8-loop 2 brother with friends
1-loop 8
2-loop 4 no brothers
6-loop 4 friends are gone
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94. Revision to looping 4- loop 4 no friends 3-loop 2 friends are gone
7-loop 2 brother with friends
8-loop 2 brother with friends
3-loop 2 friends are gone
5-loop 4 with no friends
7-loop 2 brother with friends
8-loop 2 brother with friends
1-loop 8
2-loop 4 no brothers
3-loop 2 friends are gone
6-loop 4 friends are gone
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95. My solution is better: one gate less
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99. OR Z
W is redundant in c
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107. Looped
Un-looped
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110. 7 6
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111. OK here
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