SECR1013 - Online Class #4 ( Module 4f )

Ajouté : 2026-05-30

[00:00:07]okay okay next okay uh this is another characteristic for k-map okay in k-map with four variable or more okay so this is the the maximum that we can use in our subject okay our slippers okay the topmost and the top and bottom most cell okay or column and row are adjacent okay uh adjacent okay okay so for two cells okay like this okay these two cells are addition okay to each other okay uh digestion to each other okay so if we observe carefully the binary value to that cell okay we can see here uh only one variable is different okay only one variable is different okay so for example here okay these two cell okay what is the variable the difference anyone these two cell okay this and this okay a b n k a b c d okay which variable is different okay a okay y a because it uh change from 0 okay to one okay from zero to one okay so this one okay so the difference okay see here okay only C okay C change okay from zero to one okay a B and D or zeros okay and this one okay so as to this one okay the variable that change okay is a k a okay a over here the a is zero and this a is one okay B is 0 B is the same okay so it still fulfilled the previous characteristic 4K map okay this is very important okay if this characteristic we will use to group okay uh the output to group the output okay for cell okay so first cell okay so all this cell are ejection okay all this cell are adjacent okay so you need to remember the the pattern okay you need to remember the pattern okay so later we we need to use here you will use okay uh this character characteristic okay in order to cut it okay in order to calculate uh the simplification process okay simplification process okay and itself okay itself okay so let's what we do okay we will grow yeah uh this cell become one set okay become one cell okay so for example like this okay become one set okay so this is one set okay also this is one set okay and this also we consider as one set okay one set okay all is one set okay so don't worry what is said uh what yeah I mean we've said okay later we uh I will discuss it or elaborate the grouping process okay thank you map is used to simplify the Boolean expression okay to the minimum form okay once we get the Minimus expression okay we can have the few words or less possible term okay so less possible term translate to less variable okay and in circuit design with less number of variables okay we can minimize the number of gates get to be used in the circuit okay okay so to map okay either sop or POS or space expression okay we need to do this step okay okay so for sop we need to determine the binary for product term or POS we need to determine the sum terminal the binary for some term okay after we get the binary for product term and some term okay we put either one or zero okay so one for sop zero for POS okay okay we come to the example okay so I as I mentioned uh okay so as I mentioned in okay before the break okay almost all example okay uh we use a standard form okay we use the standard form okay okay so from this expression uh we need to create the K map okay first we determine the binary okay to each product term okay so this is sop okay then we get uh this binaries okay this binaries okay so at this point okay I think I don't need to uh to mention okay how we get the debt values okay else okay uh we will go slow okay okay I really want to finish this module four okay bye tonight okay so we get the binary values okay binary combination okay and from that binaries okay we fill up okay we fill in okay the K map table okay map table okay so this is the first uh output one to the K map second okay third and fourth okay so this is the generated camera okay okay next example okay more variables okay four okay a b c and d okay determine the binary to each term okay so from that by the way we fill in okay uh to the K map okay table okay so we put one due to the expression is in sop format okay so that binary that binary okay that battery and the last uh binary combination okay so remember okay uh the cell in k-map okay uh the output actually okay are the output okay okay uh this is sop what if POS in POS okay so this expression is in POS okay so similar okay we find out the binary values okay okay and put 0 or not one pos we need to put zero okay so this is the first Zero from first term okay zero zero and then the second term zero one one over there okay third zero zero one okay and the last term okay one one one okay to to the K map okay cell okay next okay map the following expression on camera okay so this expression if we see okay it is in already in the standard form okay so this uh as your homework okay SEO homework so take note okay this is as your homework okay how to create the cat map from this expression okay so please try okay in your revision okay next uh how to map okay non-standard expression okay no standard expression okay so this part we have another characteristic okay that exists in K map whereby we can transform the non-standard equation to the standard one in more easy way okay more easy way okay so this is a numerical method okay in kmma to transform uh the expression okay become a standard form okay so this expression okay for sure it is not in standard form due to the missing variable C in the first term okay we can apply the Boolean algebra rules okay so s we can put the C variable okay in the equation okay okay so if we use the Boolean algebra okay uh we get this some terms okay okay this product term sorry this product terms okay this product terms and this is the equivalent binary values okay to each term okay so in k-map okay we can use the numerical method okay to find the missing variable okay to find the missing variable okay so a b b okay so we need to find C Okay C the one variable okay so a is one b d bar is zero okay so only one variable okay so 2 to the power of 1 is 2 okay so for C we need two combination okay zero and one okay so that's why uh we get the binary zero and one okay for a and b bar is the same okay is this the same okay that is for C Okay C okay we try to find out the missing C okay the second term okay no issue it is already in the standard form okay and if we compare okay to this binary values okay it is the same or similar if we uh transform okay the equation using the rules okay Boolean algebra rules okay Boolean algebra grows okay so again okay in this session okay I don't elaborate how we get uh this expression okay so please revise okay uh that part okay we get the similar terms okay we get the similar terms okay but more quicker okay more quick okay and then we can put okay the generated uh uh binary values okay or combination get into the K map okay into the K map okay okay next uh map the following uh expression okay on the kmm okay okay so there are missing variables okay so the first term okay the missing variable are A and D okay A and D okay so A and D are missing so a n d we see two okay two variable okay so 2 to the power of 2 is 4 okay so that's why we need to find out okay uh four combination okay so four combination is actually zero zero zero one one zero and one one okay so this is how we uh fill up okay the path for a and D A and D that means that missing okay okay the second term Okay C and D you are missing okay then we get that binaries okay uh next D okay D is missing okay we get uh this boundaries okay and the remaining terms okay uh already in the standard form okay so from the binary values okay combination that we get okay uh either we uh find out if the similar one get to delete or to be discarded to be deleted or it doesn't matter okay when we fill up the or we create the K map okay once we find get one combination is already in the K map okay we don't need to put that combination to the map okay okay so we can discard or not discard okay let's say we discard so these are the combination that we can use okay to create uh the K map okay to put into the K map okay next okay map the following uh this one is post here previous is sop okay this is the post Okay so first term the missing variable is C okay so two combination by this zero and one okay zero and one that's the binary okay next a and a or a bar or B Bar okay so the missing variables are C and D okay so four combination okay so we uh put aside here that four combination this one okay already standard or standardized okay we put okay into uh the left button okay then we fill in the okay so we put zero since this is a post expression okay okay now we come to the application okay map to simplify the Boolean expression okay so what we do to simplify okay the expression first we group The binaries okay either one or zero okay so we start first with sop so we group the binary once okay and next we determine the product term okay and the last okay okay we combine the result for product terms okay combine the result for product terms okay okay step number one okay uh to group the binaries okay to group the binary scale okay so what uh highlighted okay in red color is important okay it's important is this the characteristic in grouping the binary values okay so number one the group okay must be in this size okay one two four eight or sixteen okay other than that we cannot group the cell okay if we see here the missing uh number of cell okay is or are three five okay seven okay nine okay 11 13 okay and 15.

[00:17:02]okay okay so if we group the cell it cannot be in this uh odd numbers okay odd numbers okay only one okay is allowed yeah to Define as a group okay okay uh the second okay uh you don't need to elaborate okay it's important to to show okay how we apply uh this step number one okay okay okay the important one is we need to group okay as big as possible okay as big as possible okay so if we can see two and four sell okay so better we select four cells okay to to Define as one group okay and number three we cannot left one okay or binary one or zero in the map okay all ones must be in the group okay no one left okay in the grouping process okay and the last Point here it can be overlapped okay it can be overlapped okay so let's trade okay to the uh quick example here okay so first okay we can group okay either one two or four okay it can be like this one okay but we need to find the biggest number of cells okay for one group okay so the biggest number of cell okay is this one okay that is the first group okay and this is the second group okay so this can make we can get to group okay to group okay next okay okay so we can map we can group this K as one group okay and can we map this as one group hello class no why not I just said because it's not about ejection because it is three okay three is not counted and three is not counted okay so either we map like this okay become one group and this become one group so three groups okay three groups okay for the second K map okay so no one is left okay okay here are some other examples okay okay we can get uh three group okay okay we group this one and then this one and this one okay three group okay this okay uh we can group like this okay okay okay no okay we're gonna grow okay like that okay why because okay recall the ejection characteristic yeah okay top and bottom okay top and bottom okay so this is one group okay this is one group okay this is one group okay this is another group okay and this is another group okay so three group okay okay at the bottom and top one group and this is second this is the third one okay and this okay we need to find the maximum one okay this one one group and this is this one okay so as to this one okay so again this we got okay uh both on the side okay left and right side okay that is one group okay this is another one oh sorry okay so the last one we can group okay like this okay it can be overlapped it can be overlapped okay so this grouping is actually real simplify that the Boolean expression okay so we'll see later okay if this in this step number two it determine the minimum uh sop or terms okay from the K map okay so number one within each group okay we only choose the variable that occur in one form or in more simple word the variable that remains unchanged yeah remain and change okay number two determine the minimum product term okay for each group Okay so each group we can get one term okay one two okay we can get one term okay okay okay when the minimum product terms are derived okay we combine okay we combine to create the final expression okay so that final expression will be in simplified form okay simplified form okay so let's look to the example okay so over here we have three groups okay so the first one is the blue color okay when we write the variable or the terms it becomes a bar B bar and C bar okay and the second group okay how do we get B and C okay B and C okay either you use the truth table okay like this okay very uh simple truth table okay to to see yeah the which variable uh is unchanged okay so the rebel that I'm changed uh B and C okay B and C that's why we put B sorry B and C okay excuse me okay okay uh sorry yeah okay okay so I do we use the simple form of true stable okay like this or we can see okay uh without any uh proper method without any proper method what we can do we observe okay okay we observe okay row by row and column by column okay so we start with okay [Music] uh better not to this side to this side okay okay so it involved two rows okay so this row this row okay okay so which variable okay uh the same okay we can see this is unchanged we reflect to B okay next we go column by column okay column by column so this part okay this column doesn't exist this column okay C is unchanged Okay C is on change okay so that's why we select C okay okay we get DC here B and C okay and then we use uh in more natural how do I see it okay like this way or we use the simple truth table okay okay okay uh uh okay the purple one okay so if we transform it to the truth table get the value okay the variables are that are unchanged is a and b okay A and B okay so from this term okay we combine together okay to get the expression okay to get the expression okay so this okay become the expression okay okay number two yeah okay the blue color okay we uh put the binary okay okay and select okay the unchanged ones okay so zero we need to put the bar okay then the expression become a bar and C bar okay next the purple one okay so it is one group okay side by side okay okay so we put all the binaries yeah either you we use the binary table or we observe row by row column and by column okay so let's say we stick to the truth table way okay p is unchanged okay since B is zero okay uh we put by okay B bar and the last one a c is C so the binary is okay the values that are unchanged is a and C A A N C okay then we combine okay or this term okay become the expression okay they become the expression okay okay next uh this one okay so this black colored group okay if we observe the binary okay I think you can make it as an exercise okay uh to observe okay how do we get this a bar and C bar okay it is just a binary okay and we can observe okay only a is unchanged okay uh from the row and from the column Okay C is unchanged okay and A and C is zero that's why we put the bar okay the purple color group okay the expression become or the term become a bar and B okay the blue color okay it becomes a b bar and D okay A B bar and D okay so row by rho K A and B is unchanged okay so we put a and b but D2 B is 0 we put the bar okay and to the column okay to the column okay only D is unchanged okay D is unchanged okay one and one okay so we put d okay okay we combine all the terms okay to get the expression okay to get the expression okay okay this is another one okay uh side by side group okay where we get uh D Bar okay and the second group okay we get B and C bar okay and the third group okay we get a B bar and C okay okay next we combine okay all the terms okay all the three terms okay okay to get the expression okay to get the expression okay so on top of the slide right okay it's a note or okay if one cell okay this is okay I think don't need to explain that okay one cell that we see just now okay we can get four variable product terms okay to sell we get three variable okay so that's why here if for two cell we get three variable okay okay for itself okay itself this one cell okay per group okay we get one variable okay for cell we get two variable this is four cell okay this one okay for cell okay so we get two variable okay two variable okay okay so if all cell okay occupy okay it is one it's very straightforward yeah okay so if we have okay okay all one okay for sure we know that okay the the output yes the output is all one okay then the expression is okay one okay okay class uh can you get the idea here okay in grouping the binary 4K map hello yes sir I think uh next example maybe we just go through okay I don't need to explain okay uh it is in the textbook okay okay so we get this expression okay actually I prepared the okay this empty through stable okay to to to elaborate yeah how do we get uh these terms okay but I think it's very straightforward okay doesn't need okay to to repeat again okay to repeat okay the explanation or the elaboration okay so in your textbook okay it is in patient 137k 100 37 okay this is the second one okay we group Okay so just stick uh uh just take note okay how we do the grouping that that is important actually here okay to get the binary or the term is easier okay to grow okay uh okay one can be grouped and then okay this one okay side by side okay one group okay and this is second group okay and this is the third group okay is the expression yeah next okay uh that is one group okay so a bar and C bar this is the second group okay a bar and B and this is the last group for this game okay that's the expression okay this one okay side by side one group okay so the expression is the bar the term is D Bar sorry okay this is the second term a second group okay X the term B and C bar okay and this the last group a b bar and C okay that's the expression okay next uh use uh k-map here to minimize the following expression okay to minimize the following expression okay so first okay we find out okay the binary values okay so this is sop okay so from the boundaries uh we put the output one okay to the camera okay and then we grow the cell okay we group the cell okay so from the grouping process okay we get uh two terms here a bar and c and the second term is B Bar Okay so when we combine that two term okay it create a simplified sop expression for this expression yeah okay so here you can see here okay how they can map okay function to simplify this long string of Boolean expression become short like this one okay okay it is not a magic the nature of k-map get transformed okay the expression can become like this here become to this minimum form okay foreign how to get the cab map app from the truth table this is straightforward okay actually okay let's say uh we select output one okay output one okay output one so that is the location for this output one in in the K map okay in the K map okay so the coordinate is based on a b and c a b and c okay okay next okay don't care condition okay don't care condition okay so this is uh one characteristic uh in the kmm okay that can be further improve the simplification okay further improve the simplification okay so don't care here means uh in certain or in okay in certain problem domain okay we can have uh a set of invalid input okay set off invalid input okay invalid input okay invalid input okay invalid input okay okay so what is invalid input okay so for example uh this is a very simple one okay can you be okay at two location okay at two locations okay sorry at the same time same time same time okay can you for example you are right now in JP and at the same time you are in KL okay so it is impossible okay it is impossible okay okay B exists okay be present physical here okay physically okay so it is not uh possible like not possible okay okay and somehow the problem domain that we use in as example is about the BCD code okay so we had discussed the PCD code in it is the way how to code the integer number okay as a set of four binary digits okay four binary digit digit so BCD code use four bits okay four bits okay so four bits means uh how many combination okay 2 to the power of 4 16 right against 16 Okay so each set of four digits we represent okay in BCD here okay it will represent 0 1 2 3 4 5 up to nine okay only up to nine okay up to nine okay more than that okay let's see 10 11 and up to 16 okay become invalid okay invalid values okay for BCD application okay this is decoding application okay so we have okay zero to nine uh is 10 okay so total number of combination is 16 so there are six okay invalid combination okay so this binary is actually 10 11 up to uh 16 or not 16 15 and 15. yes we start with zero one let's start with zero okay okay so this sixth combination uh will never occur in BCD application and we can trade okay these values okay s don't care thumbs or don't care combination okay so in the application you are using K map okay this don't care uh values okay we can assign one or zero okay or simple like that okay you can assign one or zero okay since it doesn't since it will never occur okay okay so the don't care okay produce uh the better result okay so it will enlarge the group we will see in the example okay so in s sop okay for example okay the value of x or invalid okay can be treated as one okay to make the group bigger okay okay we go to the example okay so this uh actually the truth table for uh that okay apply the Obesity problem okay okay and these are the invalid input yeah okay for the problem domain okay so the invalid input when we map to the kmm okay we put to the K map okay it will be in this position okay in this position okay so we label with X we level with X okay next we observe the output one the output one okay so that output one okay the location in K map is here okay the second output one the location is here okay and the third output one okay the location is over here okay so if we group The by a big one okay the binary one okay so this is the one group okay okay so the term we can write okay S A Bar B C D okay a bar and B and C and D okay that's the uh Sumter okay and this is the second group okay so we can group uh two once okay as one group okay so the terms become a b bar and C bar okay so without don't care uh condition the expression be like this yeah okay so we take okay the terms okay from the K map okay next okay we don't care okay the expression is a or B C D okay okay so the X position okay can be grouped as one group okay why we group this is one group okay it is due to it is close to this binary one these two binary ones okay so we can simply assume okay at this point okay all X are equal to one okay so that blue group okay when we uh transform okay we settle the binary calculation we get a okay we get a okay so only a is unchanged okay only a is unchanged okay okay and next to this one okay we have one and since in don't care condition we assume okay this x it can be assumed as one then we can have okay another group okay so this green colored group okay uh when we transform into the variable it becomes b c d b c d a b c d okay okay let's look get to another example okay use can map to minimize this expression okay so in this example or exercise it will assume uh there are don't care terms okay six and seven okay six and seven okay that we can use to simplify or to group The the binaries in the kmm okay so 6 and 7 in binary okay is 1.0 and triple one okay so map all this into the K map okay map all this into the K map okay and group okay group the cell okay so it's side by side uh we get one group okay then we left okay one okay I do we select one or we can select uh this one okay but recall or remember okay the principle okay we need to find the largest one okay so in this case since we have the don't care terms okay we can assume this x okay so that's why okay we can group uh uh that column as one group okay so that column becomes C okay only C is unchanged okay and side by side group okay we get B Bar okay so the expression is D Bar or C okay plus is or operation okay okay assume uh we have don't care values okay one five eight and ten okay and we are given a k map okay we are given okay map okay and by looking to the camera okay all the output is zero okay so this is a post expression okay okay we need to minimize okay okay get the minimize expression okay okay so we put uh the don't care values okay so this is uh one group okay so recall the bottom and top and bottom condition yeah okay as we mentioned earlier okay so this is one group okay so the the term is the or D okay b or d d plus d yeah okay this is the second group okay and that is the expression okay the term okay and this is the third term Okay the third group okay and that is the expression okay and we combine all together okay so what we get is the minimum expression yeah okay the minimum expression okay so everything from the k-map is the minimum expression okay okay next uh use K map to minimize an expression Okay so this exercise okay uh uh it is in Sigma notation okay Sigma notation okay okay and the don't get terms is 0 1 and 10 okay so this is your another homework okay another homework okay another homework okay okay so we're done on sop uh expression simplification okay using K map okay next is for POS okay POS POS expression okay POS expression okay guys okay uh uh do you want to take a break hello okay we take a break okay