Digital Logic and Design CS302 Solution of Assignment 2 (Graded) Semester Fall 2013

[vuassignments]

[B]Digital Logic and Design
CS302 Assignment No. 2
(Graded)
Semester Fall 2013

Total Marks: 20
Due Date: 6th Dec 2013

Question 1 [5 Marks]

Using a karnaugh map, minimize the following POS expression:

(B+C+D) (A+B’+C+D’) (A’+B’+D’) (A+B’+C’+D’)(A+B+C’+D)(A’+B+C’+D)

(Show complete steps)
Question 2 [5Marks]

Convert the expression A’B + AC into standard SOP form and then complete the X column in the truth table mentioned below.

A B C X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

(Show complete steps)


Question 3 [10Marks]

Convert Gray code 01101111 to Binary code by showing all steps of conversion and mention which method is used for conversion?

(Show complete steps)
[/B]

[vuassignments]

how to minimize POS expression Using a karnaugh map:

Find all essential prime implicants Cover the remaining 1's/0's with as few as possible prime implicants SOP = EPIs + (as few as possible)PIs POS = (EPIs)(as few as possible PIs)

Gray Code to Binary Conversion:

This conversion method strongly follows the operation of Exclusive-OR gate. The following steps let you know how to achieve Gray Code to Binary number conversion
1. The left most significant bit of a given grey code number is same as the most left significant bit of the binary number
2. To obtain the successive binary bits to produce the equivalent binary number for the given grey code number, add the first bit of grey code to the second one and write down the result next to the first bit, add the second grey code bit to third one and write down the result and so on next to the second bit and repeat the same operation until the last bit

[chakwal]

ye lo sarkar solution cs 302 assignment 2

Question 1

Using a karnaugh map, minimize the following POS expression:

(B+C+D) (A+B’+C+D’) (A’+B’+D’) (A+B’+C’+D’)(A+B+C’+D)(A’+B+C’+D)
Ans:
Firstly convert this expression into standard POS
(A+B+C+D) (A’+B+C+D) (A+B’+C+D’) (A’+B’+C+D’) (A’+B’+C’+D’) (A+B’+C’+D’)
(A+B+C’+D’) (A’+B+C’+D)
THEN write binary values of these expression
(0000)(1000)(0101)(1101)(1111)(0111)(0010)(1010)
Now create K.map
AB/CD 00 01 11 10
00 0 1 1 0
01 1 0 0 1
11 1 0 0 1
10 0 1 1 0

Question 2

Convert the expression A’B + AC into standard SOP form and then complete the X column in the truth table mentioned below.

ANS:
A’B+AC
A’B(C+C’)+A(B+B’)C
A’BC+A’BC’+ABC+AB’C
Now write binary values of these expressions

(011)(010)(111)(101)






A B C X
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1

Question 3

Convert Gray code 01101111 to Binary code by showing all steps of conversion and mention which method is used for conversion?
Ans;

Step 1
Gray code 0 1 1 0 1 1 1 1
Binary code 0
Step 2
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1
Step 3
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0
Step 4
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0 0
Step 5
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0 0 1
Step 6
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0 0 1 0
Step 7
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0 0 1 0 1
Step8
Gray code 0 1 1 0 1 1 1 1
Binary code 0 1 0 0 1 0 1 0


END

[Xpert]

Is this the correct answer that you have just posted for cs302