CS2208b Assignment 2 Solved

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QUESTION 1 (25 marks)
Analyze the following combinational circuit by determining the values of all intermediate and final outputs for all possible inputs (16 different cases in total). Express and simplify (to the simplest sum of products expression) all intermediate and final outputs using Boolean expressions in term of A, B, C, D, Ac, Bc, Cc, and Dc, where Ac, Bc, Cc, and Dc are the complemented values of  A, B, C, and D, respectively.

 

Your answer should be in the form of a table and an expression for each output. Show all of the simplification steps and state which algebraic law you used in each step (see slide 89 and 90 in Chapter 2). R1 = 

 

 

R2 =

 

 

R3 =

 

 

R4 =

 

 

R5 =

 

 

X = 

 

 

Y =
 

 

A
B
C
D
R1
R2
R3
R4
R5
X
Y
0
0
0
0
 
 
 
 
 
 
 
0
0
0
1
 
 
 
 
 
 
 
0
0
1
0
 
 
 
 
 
 
 
0
0
1
1
 
 
 
 
 
 
 
0
1
0
0
 
 
 
 
 
 
 
0
1
0
1
 
 
 
 
 
 
 
0
1
1
0
 
 
 
 
 
 
 
0
1
1
1
 
 
 
 
 
 
 
1
0
0
0
 
 
 
 
 
 
 
1
0
0
1
 
 
 
 
 
 
 
1
0
1
0
 
 
 
 
 
 
 
1
0
1
1
 
 
 
 
 
 
 
1
1
0
0
 
 
 
 
 
 
 
1
1
0
1
 
 
 
 
 
 
 
1
1
1
0
 
 
 
 
 
 
 
1
1
1
1
 
 
 
 
 
 
 
             

QUESTION 2 (39 marks)
Analyze the following combinational circuit by determining the values of all intermediate and final outputs for all possible inputs (16 different cases in total).  Express and simplify (to the simplest sum of products expression) all intermediate and final outputs using Boolean expressions in term of A, B, C, D, Ac, Bc, Cc, and Dc, where Ac, Bc, Cc, and Dc are the complemented values of  A, B, C, and D, respectively.

 

Your answer should be in the form of a table and an expression for each output. Show all of the simplification steps and state which algebraic law you used in each step (see slide 89 and 90 in Chapter 2). R1 = 

 

 

R2 =

 

 

R3 =

 

 

R4 =

 

 

 

R5 =

 

 

R6 = 

 

 

R7 =

 

 

W  = 

 

 

X    =

 

 

Y    = 

 

 

Z = 
 

A
B
C
D
R1
R2
R3
R4
R5
R6
R7
W
X
Y
Z
0
0
0
0
 
 
 
 
 
 
 
 
 
 
 
0
0
0
1
 
 
 
 
 
 
 
 
 
 
 
0
0
1
0
 
 
 
 
 
 
 
 
 
 
 
0
0
1
1
 
 
 
 
 
 
 
 
 
 
 
0
1
0
0
 
 
 
 
 
 
 
 
 
 
 
0
1
0
1
 
 
 
 
 
 
 
 
 
 
 
0
1
1
0
 
 
 
 
 
 
 
 
 
 
 
0
1
1
1
 
 
 
 
 
 
 
 
 
 
 
1
0
0
0
 
 
 
 
 
 
 
 
 
 
 
1
0
0
1
 
 
 
 
 
 
 
 
 
 
 
1
0
1
0
 
 
 
 
 
 
 
 
 
 
 
1
0
1
1
 
 
 
 
 
 
 
 
 
 
 
1
1
0
0
 
 
 
 
 
 
 
 
 
 
 
1
1
0
1
 
 
 
 
 
 
 
 
 
 
 
1
1
1
0
 
 
 
 
 
 
 
 
 
 
 
1
1
1
1
 
 
 
 
 
 
 
 
 
 
 
             


QUESTION 3 (36 marks)
Express and simplify (to the simplest sum of products expression) all intermediate and final outputs using Boolean expressions in term of A, B, C, D, E, F, Ac, Bc, Cc, Dc, Ec, and Fc, where Ac, Bc, Dc, Ec, and Fc are the complemented values of  A, B, C, D, E, and F, respectively.

 

Your answer should be in the form of an expression for each output. Show all of the simplification steps and state which algebraic law you used in each step (see slide 89 and 90 in Chapter 2). R1 = 

 

R2 = R3 = R4 = R5 = R6 =  R7 = R8 = R9 = R10 = R11 = R12 = R 13 = R14 = R15 = G = H =