Question 2 (20 marks) An LED display is driven by four input

Question 2 (20 marks)
An LED display is driven by four input signals, A, B, C, and D. These input signals are used in combination
to create the characters on the LED display. Many LEDs make up the display, and each one needs to
convert (using logic gates) the input signals to determine when they should be on or off. The Boolean
expressions for two of the LEDs are shown below:
LED i= A ∙ B+A ∙ ( A+ C ) +B ∙( A +C)
LED j= A ∙ B ∙ D+ A ∙C ∙ D+B∙ D
a. Simplify the expressions using Boolean algebra. (8 marks)
L ED i= A ∙ B+ A ∙ ( A+C ) +B ∙ ( A +C )
L ED i= A ∙ B+ A ∙ A+ A . C+ B ∙ A+ B . C
LED i= A ∙ ( B+C )+ A+ B . C
LED i= A ( B+C +1 ) +B . C
LED i= A +B . C
LED j= A ∙ B ∙ D+ A ∙C ∙ D+B∙ D
LED j= A ∙ B ∙ D+ A ∙ B ∙C . D+ A . C . B . D+ A . B . D+ A . B . D
LED j= A ∙ B ∙ D ( 1+C ) + A . B . D+ A . B . D ( 1+C )
LED j= A ∙ B ∙ D+ A . B . D+ A . B . D
LED j= A ∙ D ( B+ B ) +¿
LED j= A ∙ D+ . B . D

b. Simulate both the original and simplified logic circuits; confirm that the results are the same. (6
marks)
Led i
Both circuits had same output for same set of inputs when tested for all input combinations

c. Convert the simplified circuit into either NANDs or NORs. Comment if this new circuit is simpler
and explain why we would want to do this conversion. (6 marks)
The converted circuits are better than previous implementation since they use only same kind of
gates. It is easier to accommodate different types of SOP equations without having to use
multiple types of gate IC for a given circuit. Also many times longest path between inputs to
output is shorter when compared to circuits using basic gates.