CODEWITHSUNDEEP
boolean-logicboolean-expressionboolean-operationsboolean-algebra
user3526197
user3526197

Reputation: 98

Boolean Expression for 4 input Logic gates

I have 4 inputs; (A, B, C, D) and 3 outputs; (X,Y,Z). 1)X is true when the input is less than 0111. 2)Y is true when the input is greater than 0111. 3)Z is true when the input is 0111.

Can someone help me out with the Boolean Expression for X? I have already obtained the expressions for Y and Z which are as follows:

Y = A
    _
Z = A . (B . C . D)

Upvotes: 1

Views: 4277

Answers (1)

Clifford
Clifford

Reputation: 93476

X is true when neither Y or Z are true:

    _   _
X = Y + Z

or

    _____
X = Y . Z

The expansion of which can be simplified, hint:

_   _   _
A + A = A

From first principles, any expression can be obtained from the truth table by OR'ing the true AND expression for each row that has a true result (then simplifying where possible); for example:

A B C   X
---------   _   _   _
0 0 0   1 = A . B . C
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 = A . B . C

     _   _   _
X = (A . B . C) + (A . B . C)

alternatively:
     _________
X = (A + B + C) + (A . B . C)

For large truth tables, this can become cumbersome (which is why my example has only three variables), in these cases a Karnaugh Map could be used instead.

Upvotes: 1

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