# Incompletely Specified Functions

Introduction
Examples

###
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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*Composed by David Belton - April 98*