Introduction to Karnaugh Maps - Combinational Logic Circuits, Functions, & Truth Tables

Summary

This video script offers a comprehensive guide on utilizing Karnaugh maps (K-maps) to simplify the process of writing Boolean functions and creating corresponding circuit diagrams. It demonstrates how to translate truth tables into K-maps for two, three, and four variables, emphasizing the importance of grouping ones in powers of two. The script also illustrates the process of deriving functions from K-maps and testing their accuracy, followed by constructing logic circuits based on the simplified functions. The tutorial encourages viewers to practice by pausing and attempting examples themselves, highlighting the efficiency of K-maps in digital logic design.

Takeaways

• 📊 The script discusses the process of using a Karnaugh map (K-map) to simplify and represent Boolean functions based on a truth table.
• 🔍 It explains how to create a three-variable K-map with eight squares, corresponding to the eight possible input combinations of variables a, b, and c.
• 📝 The importance of correctly placing the function values within the K-map squares is highlighted, which aligns with the truth table's output for each combination of inputs.
• 🔗 The concept of circling groups of ones in the K-map is introduced, emphasizing that the number of ones circled must be a power of two (1, 2, 4, 8, etc.).
• 🤔 The script illustrates how to derive Boolean expressions from the K-map by identifying variables that do not change within each group of circled ones.
• 🛠️ It demonstrates the conversion of a K-map into a circuit diagram, showing the use of AND and OR gates to represent the simplified Boolean function.
• 🔄 The video provides examples of both horizontal and vertical orientations for a three-variable K-map, as well as a four-variable K-map for more complex functions.
• 📐 The process of filling out a K-map with function values for different variable combinations is detailed, including how to handle the complements of variables.
• 🔑 The script explains how to test the derived Boolean function by substituting variable values and verifying the output against the truth table.
• 🔍 It also covers the reverse process of creating a K-map from a given Boolean function, showing how to place ones and zeros in the appropriate squares.
• 💡 Finally, the video encourages viewers to practice by pausing and attempting to create K-maps and circuit diagrams from provided truth tables or functions.

Q & A

What is a Karnaugh map and how is it used in logic design?

A Karnaugh map, often abbreviated as K-map, is a visual tool used to simplify Boolean algebra expressions and to minimize logic circuits. It is used to represent the truth table of a Boolean function in a more compact form, making it easier to identify patterns and simplify the function into its simplest form.

How many squares are needed for a three-variable Karnaugh map?

A three-variable Karnaugh map requires 2^3, which equals 8 squares, to represent all possible combinations of the three binary variables.

What is the significance of the arrangement of rows and columns in a three-variable Karnaugh map?

In a three-variable Karnaugh map, the arrangement of rows and columns corresponds to the binary values of the variables. For instance, if the variables are A, B, and C, the rows might represent A and B, while the columns represent C, allowing for a systematic representation of all possible input combinations.

How do you determine the function values to be placed in a Karnaugh map?

The function values are determined from the truth table of the Boolean function. Each cell in the Karnaugh map corresponds to a specific combination of input variables, and the value placed in that cell is the output of the function for that combination.

What is the rule for circling groups of ones in a Karnaugh map?

When simplifying a Karnaugh map, you circle groups of ones (representing TRUE or 1 in the function) together. The number of ones in a group must be a power of two, such as 1, 2, 4, or 8, because this allows for the simplest representation of the function in terms of AND and OR operations.

How do you interpret the groups of ones in a Karnaugh map to write the simplified Boolean function?

Each group of ones in a Karnaugh map corresponds to a term in the simplified Boolean function. You write down the variables that do not change within the group, and if a variable changes, you use its complement. The terms for all groups are then combined using OR operations.

What is the purpose of a circuit diagram in the context of Karnaugh maps?

A circuit diagram is used to visually represent the physical implementation of a Boolean function. After simplifying a Boolean function using a Karnaugh map, the circuit diagram shows how to connect logic gates (AND, OR, NOT) to achieve the desired output.

Can you provide an example of how to convert a simplified Boolean function into a Karnaugh map?

Certainly. If you have a simplified Boolean function like 'A BC + AB', you would create a Karnaugh map and fill in the cells where A is 1 and C is 1 for the term 'AC', and where A is 1, B is 0 for the term 'AB'. The filled cells represent the TRUE outputs of the function for the respective variable combinations.

What is the difference between a horizontal and a vertical orientation of a three-variable Karnaugh map?

The difference lies in how the variables are assigned to the rows and columns. In a horizontal orientation, one pair of variables is assigned to the rows, and the third variable to the columns. In a vertical orientation, it's the opposite, with one variable assigned to the columns and the pair of variables to the rows. The choice of orientation can affect the ease of simplifying the function.

How do you handle a four-variable Karnaugh map?

A four-variable Karnaugh map requires 2^4, or 16 squares, arranged in a 4x4 grid. Two variables are assigned to the rows and the other two to the columns. You fill in the map based on the function's truth table and then circle groups of ones to simplify the function, similar to the process with three-variable maps.

Can you explain the process of creating a circuit diagram from a simplified Boolean function?

To create a circuit diagram from a simplified Boolean function, you identify each term in the function that requires an AND operation and represents it with an AND gate. Then, you use OR gates to combine the outputs of these AND gates to represent the OR operations in the function. NOT gates may be used if any term involves a variable's complement.

Outlines

00:00

📊 Introduction to Karnaugh Maps and Truth Tables

This paragraph introduces the concept of Karnaugh maps (K-maps) as a tool for simplifying the process of writing functions based on truth tables. It explains the structure of a three-variable K-map with eight squares, each representing different input possibilities. The paragraph details how to fill in the K-map with function values from the truth table and emphasizes the importance of circling groups of ones in powers of two to simplify the function. It also provides an example of deriving a function from the K-map by identifying variables that do not change within these groups.

05:02

🔍 Testing the Function and Circuit Diagram Creation

The second paragraph continues the discussion by testing the derived function against specific variable values to ensure its correctness. It then proceeds to convert the function into a circuit diagram, explaining the use of AND and OR gates to represent the logical operations of the function. The paragraph also encourages viewers to pause and attempt the problem themselves, introducing a new example with a different K-map orientation and explaining how to fill it out based on the given truth table.

10:04

🛠 Vertical Orientation K-Map and Function Derivation

This paragraph focuses on creating a K-map with a vertical orientation, explaining the process of filling it out based on the given function values. It demonstrates how to identify pairs of ones and derive the function by considering variables that remain constant within these pairs. The paragraph also includes testing the derived function with different variable combinations to validate its accuracy and concludes with the conversion of the function into a logic circuit diagram.

15:05

🔄 Four-Variable K-Map Analysis and Function Construction

The fourth paragraph extends the concept to four-variable K-maps, guiding the viewer through the analysis of pairs of ones and the construction of a function based on constant variables within these pairs. It illustrates the process of selecting terms and building the function step by step, emphasizing the independence of certain variables for each selection. The paragraph also encourages practice by inviting the viewer to try another example with a four-variable K-map.

20:06

📚 Converting Functions into K-Maps for Different Variable Combinations

This paragraph demonstrates how to create K-maps from given functions for both three-variable and four-variable scenarios. It explains the process of identifying where variables are constant or complementary within the function terms and placing ones accordingly in the K-map. The paragraph provides examples of functions with different variable combinations and guides the viewer through the process of filling out the corresponding K-maps.

25:07

🎨 Advanced K-Map Filling with Color Coding

The final paragraph presents a more complex example of filling out a four-variable K-map based on a given function. It introduces color coding to distinguish between different terms in the function and explains the significance of the number of ones corresponding to the number of variables in each term. The paragraph concludes by summarizing the method for turning a function into a K-map and thanks the viewer for watching.

Keywords

💡Truth Table

A truth table is a mathematical table used in logic to determine the truth value of logical expressions based on the truth values of the inputs. In the video, truth tables are used to represent the different input possibilities for variables a, b, and c, and to determine the corresponding function values. For example, the script describes how to fill out a truth table for a function with three variables, where each row represents a unique combination of inputs for a, b, and c, and the last column shows the function's output for those inputs.

💡Karnaugh Map (K-Map)

A Karnaugh Map is a graphical representation used to simplify boolean algebra expressions. It is a valuable tool in digital logic design for minimizing the complexity of a circuit. The video explains how to create a K-Map from a truth table and vice versa. For instance, the script mentions a three-variable K-Map with eight squares, each corresponding to an input possibility, and demonstrates how to fill in the K-Map based on the function values from the truth table.

💡Variables

In the context of logic and the video, variables represent the inputs to a logical function, which can take on values of 0 or 1. The script discusses variables a, b, and c, and their different combinations that result in various output values. The variables are essential for constructing both the truth table and the K-Map, as they define the rows and columns of these tools.

💡Function Value

The function value is the output of a logical function given a specific set of input values. The video script describes how to place these values into the appropriate squares of a K-Map, which then helps in simplifying the function. For example, when a, b, and c are 0, 0, and 0 respectively, the function value might be 0, which is placed in the corresponding square of the K-Map.

💡Boolean Algebra

Boolean algebra is a branch of algebra dealing with binary variables and logical operations such as AND, OR, and NOT. The video uses Boolean algebra to simplify expressions derived from K-Maps. The script explains the process of converting the grouped ones in a K-Map into a simplified Boolean expression, which represents the original function in a more streamlined form.

💡Complement

In logic, the complement of a variable is the inverse of its value. If a variable is 0, its complement is 1, and vice versa. The script uses the concept of complements when discussing how to fill out a K-Map and simplify Boolean expressions. For example, if a certain variable is consistently 1 for a group of ones in a K-Map, its complement (0) is used in the simplified Boolean expression.

💡Circuit Diagram

A circuit diagram is a graphical representation of an electrical circuit. It shows the components of the circuit and their interconnections. The video script explains how to translate a simplified Boolean function into a circuit diagram, using logic gates like AND and OR gates. The script provides examples of how to create a circuit diagram based on the function derived from a K-Map.

💡AND Gate

An AND gate is a digital logic gate that outputs true or 1 only when all its inputs are true or 1. The video script describes using AND gates in circuit diagrams to represent terms in Boolean expressions that require certain conditions to be met simultaneously. For example, the term 'b AND NOT c' would require an AND gate with inputs b and the complement of c.

💡OR Gate

An OR gate is a digital logic gate that outputs true or 1 when at least one of its inputs is true or 1. In the video, OR gates are used in circuit diagrams to combine outputs from other logic gates, representing terms in Boolean expressions that require any of a set of conditions to be met. The script mentions using an OR gate to combine the outputs of AND gates to produce the final function output.

💡Simplification

Simplification in the context of the video refers to the process of reducing a Boolean expression to its simplest form using techniques such as K-Maps. The script demonstrates how to simplify expressions by grouping ones in a K-Map and then translating these groups into a minimized Boolean expression, which can then be used to design more efficient circuit diagrams.

Highlights

Introduction to using a Karnaugh map (K-map) to simplify and write a function based on a truth table.

Explanation of a three-variable K-map with eight squares representing all input possibilities.

Method to fill a K-map with function values from a truth table.

Technique for grouping ones in a K-map to simplify the function.

Rule of grouping ones in powers of two (1, 2, 4, 8, etc.) for K-map simplification.

Deriving a function from a K-map by identifying variables that do not change within a group of ones.

Example of testing the derived function against the truth table for accuracy.

Conversion of the simplified function into a circuit diagram using AND and OR gates.

Demonstration of creating a K-map with a vertical orientation for a three-variable function.

Process of filling a vertical K-map by analyzing the function values for different variable combinations.

Strategy for selecting groups of ones in a vertical K-map to form a simplified function.

Application of the derived function to create a logic circuit diagram.

Introduction to a four-variable K-map and its analysis for function simplification.

Method for identifying constant variables within groups of ones in a four-variable K-map.

Example of converting a given function into a K-map for educational purposes.

Step-by-step guide to creating a three-variable K-map from a function with terms.

Complex example of creating a four-variable K-map from a function with multiple terms.

Final example demonstrating the coloring and selection process in a four-variable K-map.

Conclusion summarizing the process of turning functions into K-maps and circuit diagrams.

Transcripts

consider the truth table shown on the

screen

how can we take the data in its truth

table and write a function using the

variables a b and c

enter carnot maps

the karnaugh map will be very helpful

for us to

write a function that describes this

truth table

so we have three variables so we need a

three variable karnaugh map with eight

squares

now the eight squares will match the

eight different input possibilities that

we have here

so this is just one of the two ways in

which we can draw a three variable

cardinal map

so we're going to have two rows

and four columns

so on top i'm going to put

for the inputs a b on the bottom c

so now the inputs a b

it could be 0 0

0 1

1 1

and 1 0. now the input for c

is only 0 or 1.

now the values that we're going to put

inside the square are the function

values that we see here

so for this first square a b is 0 and c

is 0

which corresponds to a function value of

0.

now for the next one

a b is still zero which means we're

dealing with this column

and c is one so we're dealing with this

particular square

the function value for that

is still zero

now for the third row

we can see that a b

is 0 1

and

c

is 0

and the function value is 1 so we're

going to put a 1

for that square

now for the next one a b is still 0 1

and c is 1.

so here's where a b is 0 1 and c is 1

giving us this square which the function

value is 0.

next a b is 1 0 so we're dealing with

the last column and c is zero so the

function value

is one

now for this one a b is

one zero still

c is one

and the function value is one

next we have a b is one one

so that's the third column

c is zero and the function value is one

and for the last one

the function value is zero

where a b and c is one

so that's how we can take the data in a

truth table

and put it on a karnaugh map or

for short we could say k map

now

how can we take this data and turn it

into a function

what we need to do is basically circle

groups of ones together

we can circle

one one or we could circle two ones

but we cannot circle three once

the number of ones that you can circle

could be one

two four eight

and so forth it has to be a power of two

so you can't circle three ones

five ones six ones not gonna work

so the best thing we can do is circle

two groups or two pairs of ones

let me use a different color so you can

see it

so let's start with this one

now what type of

what information can we derive from that

group of ones

those two ones highlighted do they

depend on the input a

notice that the input a varies between 0

and 1 yet the output is the same

so the output for those two

ones does it depend on a

notice that it depends on b

when b is one

the output is one so we're looking for

the variable

that doesn't change

b doesn't change

so should we write b

or not b

because b is one and the output is one

we're gonna write b

now

these two or this pair of ones also

corresponds to a c value of zero

notice that c is always zero

for

that pair of ones

so because z c is zero

and the output is one we need to write

not c

now let's move on to the next pair of

ones

so let's put an or symbol represented by

the plus sign

so

for the second pair of ones

what variables

do not change

so notice that c

changes

so for this pair of ones it is

independent of c

but notice that a b

is the same a is one b is

zero so which one is going to be not a

is it air b

so because a is one and it matches the

output function one

we're going to leave it as a but because

b is zero

we need to put

not b

because

not zero is one

so this

is the function

that explains this truth table

now we could test it out

so let's see if

a is zero and if b is one and if c is

one

if we get a function value of zero

so b is one

c is one a is zero

and b is one

so if we put

if we write the complement of one that's

going to be zero

so we have zero times one which is zero

and zero times zero is zero so we get an

output of zero

so that worked

let's try another one

let's try this one

let's see if the function will give us

the correct output

so b is zero

c is one

a is one

and b is zero

now the complement of one is zero

and the complement of zero is one

zero times zero is zero one times one is

one

zero plus one is one

so we get the right output

now for the sake of practice

let's make sure that we have the right

function let's try the last one

so b is one c is one

a is one

and b is one as well so the complement

of one is zero

and one times zero is zero zero plus

zero is zero and we can see that we have

the correct output

so we have the correct function

so that's how you could use a karnaugh

map

to quickly

write a function that corresponds to a

truth table

now let's take the function that we have

and turn it into a circuit diagram

so the function that we have was b

times the complement of c

plus a

times the complement of b

so we can write that as

b c prime plus

a

b prime

so we need an and gate to connect b and

c prime

so let's start with that

and we need another and gate

to connect

a

and b prime

so this is going to be b

and c prime and here we have a

and b prime

now notice that we have

a plus symbol between

these two terms

so we need to use an or gate

the plus symbol is associated

with the or operation

so the output of this and gate

is going to be b c prime

and the output of this and gate is going

to be

a b prime

and the output of the or gate

is going to give us the function f

which is what we have here

so that's the circuit diagram that

corresponds to this function

let's try another example

let's use this truth table

to create a k-map

and then use that to write a function

which will then use that to turn it into

a circuit diagram

if you want to pause the video and try

this problem feel free

now

the type of k-met that i'm going to draw

is going to be a little bit different

than the last one

the last one was a three variable k-map

drawn in the horizontal direction

but i'm going to draw one with

a vertical

orientation

so instead of having two rows four

columns

i'm going to have two columns

and four rows

so i'm going to put one variable above

the diagonal line

two variables below it

so a has two possibilities zero or one

bc can be zero zero

zero one one one

or one zero

so that's how you can draw a three

variable k map

with

vertical orientation

now let's fill in a table

so for this first column a is zero which

we can see it for the first four inputs

so here when b is when b and c is zero

the function is going to be zero

and when bc is 0 1

the function is going to be 1.

when bc is 1 0

the function is 0

and when bc is 1

the function is 1.

now for the second column

a is always one which will correspond to

these four

so when bc is zero

the function is one

and when bc is zero one the function is

also one

when bc is one zero the function is one

and when bc is one one the function is

zero

so that's how we can quickly fill out

this k-map

now how can we use it to write a

function for the truth table

so let's start with

this pair of ones

notice that a is always zero

so we need to write the complement of a

because the complement of zero will give

us an output of one

now for those pair of ones

notice that

b

changes

so

the output is independent of b so we're

not going to include b but notice that c

is one

so we're just going to write c

now let's draw the next pair of ones

so notice that a is always one for that

group

and this time c changes so it's

independent of c

but b is consistent b is always zero

so we're going to write b prime

now there's only one

last one that we need to consider

and that's here

so a is one we're just gonna write a

b is one we're gonna write b

and because c is zero we're gonna write

c prime

so this is the function

that corresponds to this truth table

now let's test the function to make sure

that we do indeed have the right one

so let's start with what we have here

so a is zero

c

is a zero

a is still zero b prime b is one

and then we have a b c prime so a is

zero

b is one

c is zero

the complement of zero is one

the complement of one is zero

and the complement of zero is one one

times zero is zero zero times zero is

zero

and zero times one is also zero

so this adds up to zero

which we can see that's the case

now let's try one more

let's try

this one

where a b and c is a one so we have

the complement of one times one

plus one times the complement of one

plus one times one times the complement

of one

the complement of one is a zero

so automatically zero times one is zero

one times zero is still zero

and the last one is going to be zero so

the output is once again zero

okay let's try one that's gonna give us

a value of one let's try this one

so a is one

c

is one

b is zero

and a is one

b is zero

c is one

so the complement of one is zero

the complement of zero

is one

and the complement of one is zero

zero times one is zero one times one is

one

one times zero times zero is zero

zero plus one plus zero is one

so this function works

so now you know how to write a function

using

the k-map

but now let's turn this function

into a circuit diagram

let's draw the logic circuit that

corresponds this function

so let's start with the first term that

we have

so we need an and gate

so it's going to be a prime c

and the output will be

a prime c

now for the second

and gate the input will be a

and the second input is going to be b

prime

giving us the output a

b prime

now for the last one i'm going to use a

three input and gate

so the three inputs will be a

b and c prime

now we need a three input

or gate

so then this will give us the output

function f

and so that's how you can draw

the logic circuit

for this particular function

consider the four variable k map that we

have

on the screen

go ahead and

write a function for this k-map

feel free to pause the video

so first let's begin by analyzing those

two pair of ones

so notice that a and b

is always one

for that selection

so we have a and b

and for that selection

notice that c

is always zero

but d

changes

so it depends on

c but not d

so we have a b

and since c is zero we're gonna have c

prime

now let's select another pair of ones

so let's go with that

now notice that a is always zero

so we're gonna have a prime

b changes so it's gonna be independent

of b

now c

is always one and d is always zero so

we're going to write d prime

now let's select this pair of ones that

we have there

so a is always one

and b is always zero so let's write b

prime for

for that part

now

notice that c

changes with the numbers zero and one

but d remains the same d is always one

so this is going to be a b prime d

so this is the function that corresponds

to this particular four variable k map

let's try another example

go ahead and try this one

so instead of selecting two ones we can

select a group of four ones

so for that particular group

which variables remain the same

notice that a is always 0 and b

is always 0. so we're going to have a

prime and b prime

now c

can be 0 or 1 so it's independent of c

and d can also be zero or one

so it's only going to depend on a and b

for that first selection

now the next selection

we can basically take a square of ones

so which variables are constant

notice that a is always one

so we're going to write a

b

changes between one and zero so it's

independent of b

on this side

notice that d

is always one

so it's going to depend on d

c

changes so it's independent of c

so this particular function

is represented by this equation it's a

prime b prime plus a d

so now you know how to take the

information from a four variable k map

and turn it into a function

now let's say that we're given a

function

ac

plus

a b prime

so how can we take this function

and create a three variable k map

and let's create it in the horizontal

direction

so we're gonna need two rows

and four columns

so we're gonna put a b above the

diagonal line and c below it

so a b can be 0 0

0 1

1 1 or 1 0

and c could be 0 or 1.

now let's focus on the ac term

notice that we don't have any

compliments here

so we're looking for when a is one

and when c is one

c

is one anywhere in this row

a

is one here

so what we're going to do is we're going

to put a 1

in those boxes

now let's focus on the next term

a b prime

so we just have a we're going to put one

we have the complement of b so we're

going to write zero

so let's identify

where a is one and b is zero

so this is when a is one and b is zero

so anywhere in this region

so we need to fill this row with a one

and we have an overlapping one there

now every other box

we're going to put a 0 in it

so that's how we can take a function

and draw a k map from it

now let's try another example

so let's say the function

is a

b prime

plus ac

plus a prime

bc prime

so let's create another three variable k

map

but in the vertical orientation

so we're going to have two columns

and four rows

so we're going to put the letter a on

top

bc below the diagonal line

so a can be 0 or 1

bc can be 0 0 0 1

1 1 or 1 0.

now let's start with this term a b prime

so a is going to be 1 b is going to be

0.

a is 1 in this column

so let me just highlight that in red

and b is 0

here

so that means we're going to put a 1

in those first two boxes on the right

now let's move on to the next term ac

so that's when a is one

and when c

is one

so we need to put a one here

and here

now for the next one we have a prime b c

prime

i forgot to put 1 1 for that

now for a prime we're going to write 0

for b we're going to put 1

for c prime we're going to write 0.

so a is 0

in the first column

and

b

is 1

here

and c is 0 here

so we want a

to be 0 and b to be 1 and c to be 0.

so that only corresponds to this last

square

so we're going to put

a 1 there

so every other box we're going to put a

0

and so that is the k-map

that corresponds

to that function

here's another harder example

let's say the function is a b prime

plus a prime c d

plus a

b c prime

go ahead and draw a k map for that

function

now what type of k map do we need would

you say it's a three variable k map or a

four-variable k-map

notice that we have four variables a b c

and d

so this time

we're going to need

four columns

and four rows

let's put the letters a b

on top

and c d on the bottom

so a b could be 0 0

0 1

1 1 and 1 0

and the same is true for cd

now

let's focus on

a b prime

so we have a

which we're going to put a 1 for that

and for the complement of b let's put a

zero

so one is a one and one is b zero

a is one

and b is zero

anywhere in this column

so we're gonna put a one

everywhere in that column

now let's move on to the next term

a prime c d

so let's put the zero for the complement

of a and a one for c and d

so notice that c and d is one in this

region and a

is zero

in the first two columns

so therefore we have to put a one

at the intersecting squares

now for the last term

a b c prime

we're going to put a 1 for a and b and a

0 for the complement of c

so

a and b are 1 in this region

c

is 0

in the first two

rows

so we're going to put a 1 here

everywhere else we're going to fill it

in with a zero

and so now we've completed the four

variable k map

let's work on one more example

so this one i'm going to color code

differently

so let's say the function is c

a d prime

plus

a prime b c prime d

plus a

b prime c

so go ahead and fill out the four

variable k map

given this function

so let's start with the lettuce c

so since we have c and not the

complement of c it's just going to be

one

c

is one in this region

so that's anywhere in the last two rows

so we're gonna have to put a one in

all of those rows i mean in the in those

two rows

so i'm gonna

color code this

group of eight ones

notice that when we have

just a term with one variable

we're going to get eight ones

for a term with two variables we're

going to get four ones

for a term with three variables

we're going to get two ones

and four a term with four variables

we're only going to get

one one

so let's move on to the next one

a d prime

so for a i'm gonna put one

and for d prime is zero

so a is one

in

the last two columns on the right

and d is zero

here

so we're going to have

a 1

and these as well

so now i'm going to circle those ones

with a red color

so as we can see

for a term with two variables

we have a total

of four ones highlighted in red

now let's move on to the next term

which has four variables

so we should only get

one one

in the k map

so for a prime we're gonna write zero

for b one c prime 0 d1

so

when a is 0 and b is 1 here

c

is 0 and d is 1 here

we're just going to put a 1 in this

region

and i'm going to highlight it

in green

now for the last one

a b prime c

so we're going to have a 1 for a

0 for b prime and a 1 for c

so first let's identify where

a b is 1 0

so that's going to be

in this region

and now let's identify where c

is one

c is one

in the second and the third row from the

top

so we're gonna need a one here and the

one that we already have here

so as you can see for a term with three

variables

we get a pair of ones or two ones

everything else

let's put a zero

and so now you know how to turn a

function into a k-map

so that's it for this video thanks for

watching