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Physical significance of Don't cares in Digital Logic design

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Problem Detail: 

In many Digital functions we come across don't care conditions where we use don't cares to minimize functions.
What is the significance of these don't cares in real world scenario where we actually implement the functions using logic gates?

Asked By : Ashutosh

Answered By : Akash Mahapatra

Yes they do have physical significance.
Input combinations for which value of a function ( or a device) is not specified are called don't care conditions.
They are met when the number of inputs are more than expected.
For example, conversion of binary to BCD. Both are 4 bits long but using 4 bits 16 binary numbers are possible whereas only 10 BCD numbers.

Consider another example: Suppose there are 8 locations to be addressed and we have a total of 4 address lines. To address 8 locations we only need 3 bits hence three address lines. The forth extra address line is like dont care. We actually don't care the logical value of contained in that address line.

Actually don't cares allow us to choose from a class of many functions.
Each don't care bit represents 2 values {0 or 1}, hence a function containing 'k' don't care bits correspond to a class of $2^k$ distinct functions ( as 'k' inputs can give rise to $2^k$ combinations).
The task is to choose a function out these $2^k$ functions which has the most minimal representation. Thereby decreasing the number of inputs hence making the implementation faster.

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Question Source : http://cs.stackexchange.com/questions/64965

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