CS302 ASSIGNMENT 04

ASSIGNMENT 04(cs302)

(Digital Logic Design)

Solution

Question1:

Implement the following function with a 4-to-1-line multiplexer?  Draw the truth table and the corresponding block diagram for the MUX?

                                    F(x, y, z) = ∑(1, 2, 6, 7)  

Solution:

Truth table

x	y	z	F  (Output)
0	0	0	0 1       F = z
0	0	1
0	1	0	1 0       F = z’
0	1	1
1	0	0	0 0       F = 0
1	0	1
1	1	0	1 1       F = 1
1	1	1

The 4-to-1 MUX has 2 select inputs, 4 data inputs and 1 output.  In the above truth table, variables x and y are applied to select inputs. The output (F) of truth table will be determined from values of x, y and z. For xy = 00, output F will be 1 when z = 1 and F will be equal to zero when z = 0 therefore F = z because z = 1. Similarly for xy = 01, output F will be 1 when z = 0 and F will be equal to zero when z =1 therefore F = z’ because z = 0. For xy = 10, output F will be zero for both z = 0 and z = 1 therefore F = 0. When xy = 11, output F will be 1 for both z = 0 and z = 1 therefore F = 1.          

Block diagram

In 4×1 Multiplexer, two variables x and y are applied to selection lines S₀ and S₁ in that order; x is connected to input S₁ and y is connected to input S₀. The values for data input lines are determined from truth table of function. When xy=00, the output F = z therefore variable z will be applied to data input line 0. Similarly required input to the data lines 1, 2 and 3 are determined when xy=01, 10 and 11. When xy=01, the output F = z’ therefore variable z’ will be applied to data input line 1. When xy=10, the output F = 0 therefore 0 will be applied to data input line 2. In the similar way, When xy = 11, the output F = 1 therefore 1 will be applied to data input line 3.      

                                                                            

Question2:

Implement the following function with a 8-to-1-line multiplexer with three selection lines? Draw the truth table and the corresponding block diagram for the MUX?

                                    F(A, B, C, D) = ∑(1, 3, 4, 11, 12, 13, 14, 15)                   

Solution:

Truth table

A	B	C	D	F
0	0	0	0	0 1         F = D
0	0	0	1
0	0	1	0	0 1         F = D
0	0	1	1
0	1	0	0	1 0        F = D’
0	1	0	1
0	1	1	0	0 0         F = 0
0	1	1	1
1	0	0	0	0 0         F = 0
1	0	0	1
1	0	1	0	0 1         F = D
1	0	1	1
1	1	0	0	1 1         F = 1
1	1	0	1
1	1	1	0	1 1          F = 1
1	1	1	1

The 8-to-1 MUX has 3 select inputs, 8 data inputs and 1 output.  In the above truth table, variables A, B and C are applied to select inputs. The output (F) of truth table will be determined from values of A, B, C and D. When ABC = 000, output F will be 1 when D = 1 and F will be equal to zero when D = 0 therefore F = D because output is 1 at D = 1. Similarly for ABC = 001, output F will be 1 when D = 1 and F will be equal to zero when z =0 therefore F = D because output is 1 at D = 1. When ABC = 010, output F will be 1 when D = 0 and F = 0 when D =1 therefore F = D’ because output is 1 at D = 0. When ABC = 011, output F will be 0 for both D = 0 and D = 1 therefore F = 0. When ABC = 110, output F will be 1 for both D = 0 and D = 1 therefore F = 1.          

     

Block diagram

In 8×1 Multiplexer, three variables A, B and C are applied to selection lines S₀, S₁ and S₂ in that order; variable C is connected to input S₀, B is connected to input S₁ and A is connected to input S₂. The values for data input lines are determined from truth table of function. When ABC=000, the output F = D therefore variable D will be applied to data input line 0. Similarly required input to the data lines 1, 2, 3, 4, 5, 6 and 7 are determined when ABC=001, 010 and 011, 100, 101, 110, 111. When ABC=001, the output F = D therefore variable D will be applied to data input line 1. When ABC=010, the output F = D’ therefore variable D’ will be applied to data input line 2. When ABC=011, the output F = 0 therefore 0 will be applied to data input line 3. When ABC=100, the output F = 0 therefore constant 0 will be applied to data input line 4. When ABC=101, the output F = D therefore D will be applied to data input line 5. When ABC=110, the output F = 1 therefore 1 will be applied to data input line 6. When ABC=111, the output F = 1 therefore 1 will be applied to data input line 7.