How to Detect invalid BCD input ? If It is True output should be 1 and else 0.

How to make Truth Table .

Solve this problem using K-Map.

Implement it with gates and find Expressions.

 

Quick Overview -

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. It is from 0 to 9 . This is also called "8421".

BCD takes advantage of the fact that any one decimal numeral can be represented by a four bit pattern. 

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Understand the need -

In some application if we want to whether user input is correct BCD or not then we will perform operation according to the user input either will terminate the execution or do warn the user to input correct BCD value .

 

How we are going to detect -

To solve this problem lets assume if input is from 0(0 0 0 0) to 9( 1 0 0 1) then it should indiacte true (means it is valid BCD) and if input is from 11( 1 0 1 1) to 15( 1 1 1 1) then it should inidicate false (Invalid BCD) . Now for indicaton if i assume one output , which will be high(1) for valid BCD and low(0) for Invalid , then  it can solve the problem.

So consider 4 input( BCD input) and one output to detect and make truth table .

 

Truth table -

 

Expression For K-Map -

Now from truth table , output Y will be -

Y = Σ_m ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )

 

Solve K-Map For O/P (Y) -

Y = Σ_m ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )

Represent it in 4 variable K-map.

Now From K-map we will obtain -

 Y = B₃' + B₂'B₁' 

 

Boolean Expression For Y -

 Y = B₃' + B₂'B₁' 

 

Implementation using Basic Gates -