MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 1 Simplification of SOP Expression Prime Implicant (PI) is a product which is obtained from the number of maximum minterm combination from a square next to K-map Use largest possible cluster

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 2 Simplification of SOP Expression No extra cluster

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3 Simplification of SOP Expression Algorithm 1 1.Count adjacent minterm number for each minterm in K-map 2.Choose uncovered minterm with the least adjacent minterm number. Choose only one if more than one exist 3.Execute PI for that minterm and placed inside a loop. If the minterm has been looped with more than one PI, choose PI with the most minterm number 4.Repeat step 2 and 3 until all minterm is looped

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 4 Simplification of SOP Expression Algorithm 2 1.Looped all PI in the K-map 2.Determine and choose all EPI to be looped 3.Choose minimum subset for the remained PI to complete the loop (which used to loop minterm which is not looped by the EPI)

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 5 Simplification of SOP Expression Example

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 6 Simplification of SOP Expression

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 7 Simplification of SOP Expression

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 8 Obtaining POS Expression Simplified POS expression can be obtained by collecting maxter (I.e. 0) for the given function. Example Given F=  m(0,1,2,3,5,7,8,9,10,11), we start with draw K-map, then cluster the maxterm

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 9 Obtaining POS Expression Given SOP for F’ is: To obtain POS for F, we do:

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 10 Don’t Care Condition In certain problems, some of the output is not determined The output can be ‘1’ or ‘0’ This is known as don’t care which is mark by X Example: In odd parity executor for BCD code, 6 is not used

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 11 Don’t Care Condition Don’t care condition can be used to help us in simplifying Boolean expression in K- map It can be ‘1’ or ‘0’ depends on which expression is simpler

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 12 Don’t Care Condition As a comparison –Without don’t cares –With don’t cares

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 13 Simplification of SOP Expression Example 1

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 14 Simplification of SOP Expression Example 1

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 15 Simplification of SOP Expression Example 1

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 16 Simplification of SOP Expression Example 1

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 17 Simplification of SOP Expression Example 1

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 18 Simplification of SOP Expression Example 2

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 19 Simplification of SOP Expression Example 2

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 20 Simplification of SOP Expression Example 2

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 21 Simplification of SOP Expression Example 3

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 22 Simplification of POS Expression To obtain POS expression for example 2 Draw K-map for f complement which is f’

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 23 Simplification of POS Expression To obtain POS expression for example 3 Draw K-map for f complement which is f’