Question

Make your own problem please.

1)This project will entail you each describe YOUR OWN problem (using proper sentences). You can look at Chapter 3 (Exercises 47, 48) as examples of what I mean. 2)Construct a truth table for your problem in above step. 3)Create a Boolean function (sum of products) from your truth table. 4)Reduce/simplify your Boolean function using Bool Identities (you must show all work and use at least 2 identities). 5)Create a circuit for your Boolean function in above step.

Thank you,

Answer 1

(1.) Let the problem be as follows:-

Design a combinational circuit with 3 input and 1 output, the output will be 1 when the binary value of input is less then or equal to 3, the output will be 0 otherwise.

(2.) According to above problem statement, the truth table is as follows:-

x	y	z	O
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	0

(3.) The boolean function can be derived by adding all the min terms (sum of product) whose output value is 1, hence boolean function of output is as follows:-

O = x'.y'.z' + x'.y'.z + x'.y.z' + x'.y.z

(4.) The simplification of above boolean function using bool identities are as follows:-

In this simplification we are using distributive and complementarity law, which states as follows:-

1. Distributive law A.(B+C) = A.B + A.C
2. Complementarity/ OR law A+A' = 1

O = x'.y'.z' + x'.y'.z + x'.y.z' + x'.y.z

=> O = x'.y'.(z'+z) + x'.y.(z'+z) ............(Using distributive law)

=> O = x'.y'.1 + x'.y.1 .................(Using Complementarity/ OR law)

=> O = x'.y' + x'.y

=> O = x'.(y'+y) .................(Using distributive law)

=> O = x'.1 ...............(Using Complementarity/ OR law)

=> O = x'

(5.) The circuit using above boolean function is as follows:-

Х Y Z 0 =