# Incompletely Specified Functions

Introduction

### Introduction

Incompletely specified functions, also known as can't happen conditions, is a situation that sometimes occurs when certain combinations of the variables of a function cannot occur. For these combinations we can select the value of the function to be 0 or 1; whichever leads to the more minimal solution.

Related below is a situation where for certain combinations of the variables one does not care what the value of the function becomes (either 0 or 1).

For these can't happen and don't care situations the Karnaugh map entry is X indicating that the particular cell can be taken either as 0 or 1.

### Examples

A binary coded decimal counter, having four output lines, is connected to a logic network. It is required that the output of the network be logic 1 whenever there are two or more input lines at logic 1. Also, for the binary coded decimal number 0001, the output value is of no importance.

A binary coded decimal number has values ranging from 0000 to 1001 (decimal 0 to 9) the values 1010 to 1111 (decimal 10 to 15) never occurs. Let the logic network have inputs A, B, C, D where A is connected to the most significant digit of the binary coded decimal number and D to the least significant. The output from the logic network will be:

Z = f(A, B, C, D) = (0011,0101,0110,0111,1001) = (3,5,6,7,9).

With can't happen conditions: (1010, 1011, 1100, 1101, 1110, 1111) = (10, 11, 12, 13, 14, 15)

and the don't care conditions: (0001)

Entering this on a Karnaugh map:

The required function is therefore: Z = f(A, B, C, D) = BC + D

Check if the above function is right.

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