PAL

PPT on PAL

1. SYED HASAN SAEED [email protected] https://shasansaeed.yolasite.com 1 Syed Hasan Saeed, Integral University, Lucknow

2. PROGRAMMABLE ARRAY LOGIC (PAL) Syed Hasan Saeed, Integral University, Lucknow 2

3. PROGRAMMABLE ARRAY LOGIC (PAL): The PAL is a programmable logic device with programmable AND gates followed by fixed OR gates. For designing of PAL, the Boolean function must be in simplified form. Product term cannot be shared with two or more OR gates, it means that each function can be simplified by itself. Syed Hasan Saeed, Integral University, Lucknow 3

4. PAL With 4 Inputs, 4 Outputs, three wide AND-OR structure: 4 F 1 F 2 F 3 F 4 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 Product term I 1 I 2 I 3 I 4 Fig. 1

5. EXAMPLE: Design a combinational circuit using a suitable PAL considering the following Boolean expression. Use a PAL with four inputs, four outputs and three wide AND-OR structure. w(A,B,C,D) = ∑m (2,12, 13) x(A,B,C,D) = ∑m (7,8,9,10,11,12,13,14,15) y(A,B,C,D) = ∑m (0,2,3,4,5,6,7,8,10,11,15) z(A,B,C,D) = ∑m (1,2,8,12,13) SOLUTION: STEP 1: Minimize by K-map Syed Hasan Saeed, Integral University, Lucknow 5 1 1 1 1 1 1 1 1 1 1 1 1 AB CD AB CD 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10

6. K-maps Syed Hasan Saeed, Integral University, Lucknow 6 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10 1 1 1 1 1 1 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10 w

7. Given that Input = 4 , Output =4 and three wide AND-OR structure, it means each output expression must contain at most three product terms. In z , there are four product terms, we can reduced to three by substituting in the expression of z. The output ‘w’ and ‘x’ having two terms. So one AND gate of w and x will remain unused. For unused AND gates, leave all its input fuse intact (always = 0) Syed Hasan Saeed, Integral University, Lucknow 7

8. PAL Programming table: 8 Product terms no. Product terms AND Inputs Outputs A B C D w 1 1 1 - - 2 1 - 3 -- - - - - - 4 A 1 - - - - 5 BCD - 1 1 1 - 6 -- - - - - - 7 1 - - - 8 CD - - 1 1 - 9 - - - 10 w - - - - 1 11 1 - 12 1 -

9. PAL With 4 Inputs, 4 Outputs, three wide AND-OR structure: 9 w x y z A B C D w 1 2 3 4 5 6 7 8 9 10 11 12 Product term A B C D Fig. × × Unused AND gates are indicated by ‘ × ’ This buffer generates w and × × × × × × × × × × × × × × × × × × × × × × × × × ×

10. EXAMPLE: Implement the following Boolean functions using suitable PAL w(A,B,C,D) = ∑m (1,3,4,6,9,11,12,14) x(A,B,C,D) = ∑m (1,3,4,6,9,11,12,14,15) y(A,B,C,D) = ∑m (0,2,4,6,8,12) z(A,B,C,D) = ∑m (2,3,8,9,12,13) SOLUTION: Simplify by K-maps 10 1 1 1 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10 1 1 1 1 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10 w

11. K-maps: Syed Hasan Saeed, Integral University, Lucknow 11 1 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10 1 1 1 1 1 1 AB CD 00 01 11 10 00 01 11 10

12. PAL Programming Table: Syed Hasan Saeed, Integral University, Lucknow 12 Product Term No. Product Terms AND Inputs Outputs A B C D w 1 - - 1 - 2 - 1 - - 3 w - - - - 1 4 ABC 1 1 1 - - 5 - - - 6 - - - 7 1 - - - 8 1 - -

13. PAL With 4 Inputs, 4 Outputs, two wide AND-OR structure: 13 w x y z A B C D w 1 2 3 4 5 6 7 8 Product term A B C D Fig. This buffer generates w and × × × × × × × × × × × × × × × × ×

14. EXAMPLE : Implement the following Boolean functions using suitable PAL x(A,B,C) = ∑ m (2,3,5,7) y(A,B,C) = ∑ m (0,1,5) z(A,B,C) = ∑ m (0,2,3,5) SOLUTION: Minimize the function by K- map: Syed Hasan Saeed, Integral University, Lucknow 14 1 1 1 1 A BC 00 01 11 10 1 1 1 1 A BC 00 01 11 10 1

15. K-Map: Syed Hasan Saeed, Integral University, Lucknow 15 1 1 1 1 A BC 00 01 11 10 1 NOTE: Here all product terms contains two input except in ‘z’ it has maximum three inputs A,B and C. So there is three wide i.e. each section must have three AND gates. Logic diagram is shown in fig.

16. PAL With 4 Inputs, 4 Outputs, three wide AND-OR structure: 16 x y z A B C D 1 2 3 4 5 6 7 8 9 Product term A B C D Fig. × Unused AND gates are indicated by ‘ × ’ × × × × × × × × × × × × × × × ×

17. THANK YOU Syed Hasan Saeed, Integral University, Lucknow 17