Digital Logic and Design Vishal Jethva Lecture No. 10 svbitec.wordpress.com.

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Presentation transcript:

Digital Logic and Design Vishal Jethva Lecture No. 10 svbitec.wordpress.com

Recap Examples of Boolean Analysis of Logic Circuits Examples of Simplification of Boolean Expressions Standard form of SOP and POS expressions svbitec.wordpress.com

Recap Need for Standard SOP and POS expressions Converting standard SOP-POS Minterms & Maxterms Converting SOP & POS to truth table format svbitec.wordpress.com

Karnaugh Map Simplification of Boolean Expressions Doesn’t guarantee simplest form of expression Terms are not obvious Skills of applying rules and laws K-map provides a systematic method An array of cells Used for simplifying 2, 3, 4 and 5 variable expressions svbitec.wordpress.com

3-Variable K-map AB\C A\BC svbitec.wordpress.com

4-Variable K-map AB\CD svbitec.wordpress.com

Grouping & Adjacent Cells K-map is considered to be wrapped around All sides are adjacent to each other Groups of 2, 4, 8,16 and 32 adjacent cells are formed Groups can be row, column, square or rectangular. Groups of diagonal cells are not allowed svbitec.wordpress.com

Mapping of Standard SOP expression Selecting n-variable K-map 1 marked in cell for each minterm Remaining cells marked with 0 svbitec.wordpress.com

Mapping of Standard SOP expression SOP expression AB\C A\BC svbitec.wordpress.com

Mapping of Standard SOP expression SOP expression AB\CD svbitec.wordpress.com

Mapping of Non-Standard SOP expression Selecting n-variable K-map 1 marked in all the cells where the non- standard product term is present Remaining cells marked with 0 svbitec.wordpress.com

Mapping of Non-Standard SOP expression SOP expression AB\C A\BC svbitec.wordpress.com

Mapping of Non-Standard SOP expression SOP expression AB\C A\BC svbitec.wordpress.com

Mapping of Non-Standard SOP expression SOP expression AB\CD svbitec.wordpress.com

Mapping of Non-Standard SOP expression SOP expression AB\CD svbitec.wordpress.com

Mapping of Non-Standard SOP expression SOP expression AB\CD svbitec.wordpress.com

Simplification of SOP expressions using K-map Mapping of expression Forming of Groups of 1s Each group represents product term 3-variable K-map 1 cell group yields a 3 variable product term 2 cell group yields a 2 variable product term 4 cell group yields a 1 variable product term 8 cell group yields a value of 1 for function svbitec.wordpress.com

Simplification of SOP expressions using K-map 4-variable K-map 1 cell group yields a 4 variable product term 2 cell group yields a 3 variable product term 4 cell group yields a 2 variable product term 8 cell group yields a 1 variable product term 16 cell group yields a value of 1 for function svbitec.wordpress.com

Simplification of SOP expressions using K-map AB\C A\BC svbitec.wordpress.com

Simplification of SOP expressions using K-map AB\C A\BC svbitec.wordpress.com

Simplification of SOP expressions using K-map AB\CD svbitec.wordpress.com

Simplification of SOP expressions using K-map AB\CD svbitec.wordpress.com

Simplification of SOP expressions using K-map AB\CD svbitec.wordpress.com

Mapping Directly from Function Table Function of a logic circuit defined by function table Function can be directly mapped to K-map svbitec.wordpress.com

Mapping Directly from Function Table InputsOutput ABCDF InputsOutput ABCDF svbitec.wordpress.com

Mapping Directly from Function Table AB\CD svbitec.wordpress.com

Don’t care Conditions Some input combinations never occur Outputs are assumed to be don’t care Don’t care outputs used as 0 or 1 during simplification. Results in simpler and shorter expressions svbitec.wordpress.com

Don’t Care Conditions InputsOutput ABCDF InputsOutput ABCDF X 1011X 1100X 1101X 1110X 1111X svbitec.wordpress.com

Don’t Care Conditions AB\CD xxxx 1000xx svbitec.wordpress.com

Don’t Care Conditions AB\CD xxxx 100xxx svbitec.wordpress.com

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