Chapter 2

// Questions

Covert the following expressions to normal form
- F(A,B)=B
- F(A,B,C)=AB+BC
- F(A,B,C)=A+BC
- F(A,B,C)=A+C
- F(A,B,C)=ABC+A+BC
- F(A,B,C)=AB+BC
- F(A,B,C,D)=AB+AC
- F(A,B,C,D)=(B D)+AC
Expand the following expression into normal form and express as sum-of-products:
```
    F(X,Y,Z)=XYZ+(X Y Z)+YZ
```
Represent the expression above in product-of-sums form.
Implement the expression in question 2 using AND and OR gates
Implement the resulting POS equation from 3 using AND and OR gates
Express the following equation in SOP form:
F(A,B,C)=(A+B+C)(A+B+C)(A+B+C)
Express the following in maxterm shorthand form:
```
    F(A,B,C,D)=(A+B+D)(A+B+C)(A+B+D)(B+C+D)
```

Using the truth table produce:

Repeat the question above producing a POS implementation to include:
- POS equation for F
- Maxterm shorthand equation for F
- Logic diagram for POS implementation
Implementing the function in question 2 would be difficult as there are no standard TTL OR gates available with more than 2 inputs. Produce logic diagrams illustrating how to make the following:
- A three-input OR gate using two input OR gates
- A four-input OR gate using two-input OR gates
There are AND gates available with more than two inputs, but if only two-input AND gates were available, illustrate how to make the following:
- A three input AND gate using 2 two-input AND gates
- A four input AND gate using 2 two-input AND gates
Convert the following to the other normal form:
- F(x,y,z)=∑m(1,3,7)
- F(w,x,y,z)=∑m(0,2,6,11,13,14)
- F(x,y,z)=Πm(0,6,3,7)
- F(w,x,y,z)=Πm(0,1,2,3,4,6,12)
Express the following functions in SOP and POS forms:
- F(A,B,C)=(A+B)•(B+C)
- F(x,y,z)=(xy+z)(y+xz)
Given the folowing boolean functions for F and G, obtain the truth table for F+G

F=D+ABC+AC
G=D(A+B)(A+C)

Covert the following expressions to normal form

Expand the following expression into normal form and express as sum-of-products:
```
    F(X,Y,Z)=XYZ+X Y Z+YZ
```
F(X,Y,Z)=( X Y Z)+(XYZ)+(XYZ)+(XYZ)
Represent the expression above in product-of-sums form.

F(X,Y,Z)= (X+Y+Z)• (X+Y+Z)• (X+Y+Z)• (X+Y+Z)
Implement the expression in question 2 using AND and OR gates
Implement the resulting POS equation from 3 using AND and OR gates
Express the following equation in SOP form:
```
    F(A,B,C)=(A+B+C)(A+B+C)(A+B+C)
```
F=(A B C)+ (A BC)+ (ABC) +(ABC)+ (ABC)
Express the following in maxterm shorthand form:
```
    F(A,B,C,D)=(A+B+D)(A+B+C)(A+B+D)(B+C+D)
```
Πm(2,3,8,10,11,13,15)

Using the truth table produce:

SOP for f	A BC+ABC+AB C+ABC
Minterm shorthand equation for F	∑m(1,2,4,7)
Logic diagram for SOP implementation<

Repeat the question above producing a POS implementation to include:

POS for f (A+B+C)•(A+B+C)•(A+B+C)•(A+B+C)

Maxterm shorthand equation for F Πm(1,2,4,7)

Logic diagram for POS implementation
Implementing the function in question 2 would be difficult as there are no standard TTL OR gates available with more than 2 inputs. Produce logic diagrams illustrating how to make the following:
- A three-input OR gate using two input OR gates
- A four-input OR gate using two-input OR gates
There are AND gates available with more than two inputs, but if only two-input AND gates were available, illustrate how to make the following:
- A three input AND gate using 2 two-input AND gates
- A four input AND gate using 2 two-input AND gates

Convert the following to the other normal form:

(x yz)+ (xyz)+(xyz)

(wx y z)+ (wxyz)+ (wxyz)+ (wxyz)+ (wxyz)+(wxyz)

(x+y+z) (x +y+z) (x+y+z) (x+y+z)

(w+x+y+z) (w+x+y+z) (w+x+y+z) (w+x+y+z) (w+x+y+z) (w+x+y+z) (w+x+y+z)

Given the folowing boolean functions for F and G, obtain the truth table for F+G

Source: Passafine, John and Michael Douglas, Digital Logic Design

POS for f	(A+B+C)•(A+B+C)•(A+B+C)•(A+B+C)
Maxterm shorthand equation for F	Πm(1,2,4,7)
Logic diagram for POS implementation