National University of Computer & Emerging Sciences, Lahore
Department of Electrical Engineering (Spring 2024)
EE1005 – Digital Logic Design (BCS-2E, BCS-2F, BDS-2A)
Assignment#1
Due Date: February 20, 2024
Question#1: CLO-01
Convert the following numbers from the given base to the other three bases listed in the table:
Decimal Binary Octal Hexadecimal
367.8125
101001101.0101
A7CF.D
Question#2: CLO-02
A) Draw logic diagram for the following Boolean functions:
F 1=CD+ B( A + DC )
F 2=C(B+ A)
F 3= AB(B+ D)B C + AC
F 4=(CD+ B)( A+C )
B) Find level of implementation of each logic circuit drawn in part (A).
C) Which of the Boolean functions are equivalent.
Question#3: CLO-02
Optimize the following Boolean expressions using algebraic manipulation.
a) x + xyz+ x yz +wyx + x y + w x y
b) A BC +( A +B+ C)+ A B C D
c) ( B+BC ) ( B+ B C )( B+ D )
d) A BCD + A BCD+ BCD+ AB
Question#4: CLO-02
Optimize the following Boolean expressions using K-map:
a) A BC D+ A B C D+ A B C D+ A BC D+ AB C D+ A B C D+ ABCD
b) ( A+ B+C )( A+ B+C ) ( A+ B+C ) ( A+ B+C )( A+ B+C ) ( A + B+C )
, National University of Computer & Emerging Sciences, Lahore
Department of Electrical Engineering (Spring 2024)
Question#5: CLO-02
Use Karnaugh map to find both minimal SOP and POS expressions for the following Boolean
functions:
a) F ( A , B ,C , D ) =∑ m ( 0,1,4,5,6,7,8,9,12 ,1 4 )
b) F ( w , x , y , z )=∏ M (1,3,9,11,12,14)
c) F ( A , B ,C , D ) =∑ m (2,3,4,6,10,12 ) , d ( A , B ,C , D )=∑ m ( 0,5,8,11,13 )
d) F ( w , x , y , z )=∑ m ( 1,3,4,6 , 11, 1 4 , 1 5 )
Question#6: CLO-02
A Careem Chauffeur Service has been started in Lahore. The company is promoting its service
by providing limited amount of free credit to its clients in order to use its pick and drop service
by opening an account. However, the free credit can be earned under certain conditions.
Moreover, the credit may be 1000Rs, 350Rs, or 100Rs depending upon the fact that how the
account has been created. The details are as under:
1) If the account is created without any reference of Careem’s client then no credit will be
given.
2) If the account is created using reference of Careem’s client then 100Rs. credit will be
given.
3) If first ride is requested by an account created through reference, but the reference was
sent before January 10, 2016 then earned credit would be 1000Rs. otherwise the earned
credit will be 350Rs.
You are required to design a digital system indicating what amount of free credit a Careem’s
client has earned.
Show all necessary steps to reach optimal design for the required system, from truth table to
circuit diagram.
Hint: Choose appropriate binary code to represent each amount.
Question#7: CLO-02
You are required to design a digital circuit that takes three numbers ‘x’ (1 bit) and ‘y’ (2 bit) and
‘z’ (1 bit) as input and checks that whether the applied input satisfies the following inequality
equation or not.
2 x+3 y + z ≥5
Show all necessary steps to design the required system optimally, from truth table to circuit
diagram.
Department of Electrical Engineering (Spring 2024)
EE1005 – Digital Logic Design (BCS-2E, BCS-2F, BDS-2A)
Assignment#1
Due Date: February 20, 2024
Question#1: CLO-01
Convert the following numbers from the given base to the other three bases listed in the table:
Decimal Binary Octal Hexadecimal
367.8125
101001101.0101
A7CF.D
Question#2: CLO-02
A) Draw logic diagram for the following Boolean functions:
F 1=CD+ B( A + DC )
F 2=C(B+ A)
F 3= AB(B+ D)B C + AC
F 4=(CD+ B)( A+C )
B) Find level of implementation of each logic circuit drawn in part (A).
C) Which of the Boolean functions are equivalent.
Question#3: CLO-02
Optimize the following Boolean expressions using algebraic manipulation.
a) x + xyz+ x yz +wyx + x y + w x y
b) A BC +( A +B+ C)+ A B C D
c) ( B+BC ) ( B+ B C )( B+ D )
d) A BCD + A BCD+ BCD+ AB
Question#4: CLO-02
Optimize the following Boolean expressions using K-map:
a) A BC D+ A B C D+ A B C D+ A BC D+ AB C D+ A B C D+ ABCD
b) ( A+ B+C )( A+ B+C ) ( A+ B+C ) ( A+ B+C )( A+ B+C ) ( A + B+C )
, National University of Computer & Emerging Sciences, Lahore
Department of Electrical Engineering (Spring 2024)
Question#5: CLO-02
Use Karnaugh map to find both minimal SOP and POS expressions for the following Boolean
functions:
a) F ( A , B ,C , D ) =∑ m ( 0,1,4,5,6,7,8,9,12 ,1 4 )
b) F ( w , x , y , z )=∏ M (1,3,9,11,12,14)
c) F ( A , B ,C , D ) =∑ m (2,3,4,6,10,12 ) , d ( A , B ,C , D )=∑ m ( 0,5,8,11,13 )
d) F ( w , x , y , z )=∑ m ( 1,3,4,6 , 11, 1 4 , 1 5 )
Question#6: CLO-02
A Careem Chauffeur Service has been started in Lahore. The company is promoting its service
by providing limited amount of free credit to its clients in order to use its pick and drop service
by opening an account. However, the free credit can be earned under certain conditions.
Moreover, the credit may be 1000Rs, 350Rs, or 100Rs depending upon the fact that how the
account has been created. The details are as under:
1) If the account is created without any reference of Careem’s client then no credit will be
given.
2) If the account is created using reference of Careem’s client then 100Rs. credit will be
given.
3) If first ride is requested by an account created through reference, but the reference was
sent before January 10, 2016 then earned credit would be 1000Rs. otherwise the earned
credit will be 350Rs.
You are required to design a digital system indicating what amount of free credit a Careem’s
client has earned.
Show all necessary steps to reach optimal design for the required system, from truth table to
circuit diagram.
Hint: Choose appropriate binary code to represent each amount.
Question#7: CLO-02
You are required to design a digital circuit that takes three numbers ‘x’ (1 bit) and ‘y’ (2 bit) and
‘z’ (1 bit) as input and checks that whether the applied input satisfies the following inequality
equation or not.
2 x+3 y + z ≥5
Show all necessary steps to design the required system optimally, from truth table to circuit
diagram.
