AOI Logic Implementation. Digital Electronics

Transcription

1 AOI Logic Implementation Digital Electronics

2 AOI Logic Implementation This presentation will demonstrate how to: 1) Design an AOI logic circuit from a Sum-Of- Products (SOP) logic expression. OUT A B B C EQUALS Logic Expression AOI Logic Circuit 2

3 AOI Logic Implementation This presentation will also demonstrate how to: 2) Design an AOI logic circuit from a Product-Of- Sums (POS) logic expression. OUT A B B C EQUALS Logic Expression AOI Logic Circuit 3

4 Sum-Of-Products (SOP) Sum-of-Products is one of two ways to create a logic expression. A logic expression, in SOP form, shows all of the input combinations that produce a logic 1 output. These combinations of input variables are known as Minterms. 4

5 Sum-Of-Products (SOP) In a Sum-of-Products expression the Minterms are summed (OR ed) together. SOP expressions can easily be implemented as a set of AND gates feeding into a single OR gate. Example: F 2 A B CD B CD A B 5

6 Designing AOI SOP Logic Circuits Three (3) Design Steps 1) Implement each Minterm in the logic expression with an AND gate with the same number of inputs as there are variables in the Minterm. (i.e., AB = 2 input gate, ABC = 3 input gate, ABCD = 4 input gate, etc.) 6

7 Designing AOI SOP Logic Circuits Three (3) Design Steps 2) OR together the outputs of the AND gates to produce the logic expression. 3) If necessary, gates can be cascaded to create gates with more inputs. 7

8 Example #1: AOI Implementation SOP Design an AOI Logic Circuit for the SOP logic expression shown below. F 2 A B CD B CD A B 8

9 Example #1: AOI Implementation SOP Solution: F 2 A B CD B CD A B 9

10 Example #1: AOI Implementation SOP Unfortunately, in this class, we only have access to (2) input OR gates and (2) & (3) input AND gates. Limiting your design to these gates, redesign the AOI Logic Circuit for the SOP expression in the previous example. 10

11 Example #2: AOI Implementation SOP Solution: Redesigned using 2-3 input gates only. 11

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13 Product-Of-Sums (POS) Product-of-Sum (POS) is another way to create a logic expression. A logic expression, in POS form, is the complement of the SOP form. 13

14 Product-Of-Sums (POS) A logic expression, in POS form, shows all the input combinations that produce a logic 0 output. These combinations of input variables are known as Maxterms. 14

15 Product-Of-Sums (POS) In a Product-Of-Sums expression, the Maxterms are multiplied (AND ed) together. POS expressions can be implemented as a set of OR gates feeding into a single AND gate. F 4 Example: W X Y Z W X Y W Z 15

16 Designing AOI POS Logic Circuits Three (3) Design Steps 1. Implement each Maxterm in the logic expression with an OR gate with the same number of inputs as there are variables in the Maxterm. (i.e., A+B = 2 input gate, A+B+C = 3 input gate, A+B+C+D = 4 input gate, etc.) 16

17 Designing AOI POS Logic Circuits Three (3) Design Steps 2. AND together the outputs of the OR gates to produce the logic expression. 3. If necessary, gates can be cascaded to create gates with more inputs. 17

18 POS Logic Expression From Truth Table Write the Maxterm adjacent to every row in the truth table that contains a zero in the output column. Write the Product of Sums (POS) logic expression by multiplying together all of the Maxterms. Example: Write the POS logic expression for the output F 5 in the truth table below. X Y Z F X+Y+Z X+Y +Z X +Y+Z X +Y +Z F 5 = (X+Y+Z) (X+Y +Z) (X +Y+Z ) (X +Y +Z ) Maxterms POS Logic Expression 18

19 Another example: Truth Table for AOI POS Logic Circuits A B C F Maxterms (A+B) (A+B +C) (A +B ) Truth Table for POS is the complement of SOP Maxterms are zero output levels Input levels are reversed (eg. a zero is X and a 1 is X ) Inputs are summed to make the maxterm Maxterms are multiplied to get the logic statement F 1 = (A+B) (A+B +C) (A +B ) POS Logic Expression In this case, SOP logic is simpler: F 1 = A BC + AB C 19

20 Example #3: AOI Implementation POS Design an AOI Logic Circuit for the POS logic expression shown below. F 4 W X Y Z W X Y W Z 20

21 Example #3: AOI Implementation POS Solution W X Y Z W X Y W Z F 4 21

22 Example #4: AOI Implementation POS Limiting your design to only (2) input OR gates and 2-3 input AND gates, redesign the AOI Logic Circuit for the POS logic expression in the previous example. 22

23 Example #4: AOI Implementation POS Solution 23

24 The End! 24