Elec 2607 Digital Switching Circuits Lecture 17 & 18: Digital Logic 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 0:

ANOTHER FORM OF Digital Logic 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

AND Gates No x indicates use a 1 OR Gates No x indicates use a 0 24/11/2018 ELEC 2607 Lecture 17 & 18:

Wrong drawing X X X AND Gates No x indicates variable disabled use a 1 OR Gates No x indicates variable disabled use a 0 24/11/2018 ELEC 2607 Lecture 17 & 18:

No x indicates variable disabled use a 1 AND Gates No x indicates variable disabled use a 1 OR Gates No x indicates variable disabled use a 0 24/11/2018 ELEC 2607 Lecture 17 & 18:

No x indicates variable disabled use a 1 AND Gates No x indicates variable disabled use a 1 OR Gates No x indicates variable disabled use a 0 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

Slide taken from Lecture 0 This stuff again 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

Change the way it looks Same as in middle 24/11/2018 ELEC 2607 Lecture 17 & 18:

ELEC 2507 ELEC 2507 24/11/2018 ELEC 2607 Lecture 17 & 18:

5V 5V 5V 24/11/2018 ELEC 2607 Lecture 17 & 18:

5V 5V 5V 5V 5V 24/11/2018 ELEC 2607 Lecture 17 & 18:

5V 0V 0V 5V 5V 5V 5V 5V 5V 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

What ‘s the function What ‘s the function 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

AND Gates No x indicates use a 1 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

disconnect disconnect Put into sum of products form X P = AB+ACD X X X X disconnect disconnect 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

disconnect 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

Read carefully and REMEBER Key to PLA design 24/11/2018 ELEC 2607 Lecture 17 & 18:

Obvious looping Needs explaining 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

A GOOD PLACE TO TAKE A BREAK 1 2 3 4 5 Only have 5 and terms available 24/11/2018 ELEC 2607 Lecture 17 & 18: A GOOD PLACE TO START AGAIN

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 15 & 16:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

Think about: “who can design the circuit sung the least number of 2 input Mux’s 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

a b c d 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 1 d d 1 1 d d 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d X e f g W Map Key Y Try something ??????????????????? 24/11/2018 ELEC 2607 Lecture 17 & 18:

a b c d 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 No other options for the 1/d pair in “d” segment. Loop of 2 is the best we can do. But we can share d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 4 times d d d d d d 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 One possible looping with this one. Can be shared 4 times d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 4 times d d d d d d 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d One possible looping with this one. Can be shared 4 times d d d d d d d d d d 1 d d 1 1 d d 1 1 d d X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 4 times 1 d d 1 1 d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d One possible looping with this one. Can be shared 4 times 1 d d 1 1 d d 1 1 d d X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 5 times X e f g W 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d One possible looping with this one. Can be shared 5 times X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 2 times X e f g W 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d One possible looping with this one. Can be shared 2 times X e f g W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 4 times X e f g W 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d One possible looping with this one. Can be shared 4 times X e f g W b is done c is done d is done Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 3 times. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d One possible looping with this one. Can be shared 3 times. Group of 8 is largest looping that I can share X e f g W a is done b is done c is done d is done f is done g is done Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

One possible looping with this one. Can be shared 2 times. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 1 d d 1 1 d d 1 d d 1 d d Z 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d X e f g W Extend previous group of 2 “Red” to a group of 4. Larger loop = simpler and term a is done b is done c is done d is done e is done f is done g is done One possible looping with this one. Can be shared 2 times. Group of 4 is largest looping that I can share Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

a b c d 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d d d d d d d d d d d d d d d 1 1 d d 1 1 d d 1 1 d d 1 d d 1 1 1 1 1 Z 1 1 1 1 1 1 1 1 d d d d d d d d d d d d 1 d d 1 1 d d 1 1 d d e f g X 9 loops W Map Key Y 24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18:

24/11/2018 ELEC 2607 Lecture 17 & 18: