lilSection 4-5 I Kamaugh Map Method

l
i
l

Section 4-5 I Kamaugh Map Method 6 131

The K map is now filled agd ca_n be_looped for simplification. Verify that
proper looping producesy= A5 + C + D.



“Don't-Care” Conditions

Some logic circuits can be designed so that there are certain input conditions for
which there are no specified output levels, usually because these input conditions
will never occur. In other words, there will be certain combinations of input levels
where we “don‘t care" whether the output is HIGH or LOW. This is illustrated in the
truth table of Figure 4-18(a).

Here the output 2 is not specified as either 0 or 1 for the conditions A, B, C =
l, 0, 0 and A, B, C = 0, l, l. InSIead, an xis shown for these conditions. The xrep-
resents the don't-care condition. A don’t-care condition an come about for sev-
eral reasons, the most common being that in some situations certain input combi-
nations can never occur. and so there is no specified output for these conditions.

A circuit designer is free to make the output for any don’t-care condition either
a 0 or a l in order to produce the simplest output expression. For example, the K
map for this truth table is shown in Figure 4-18(b) with an xplaced in the A35 and
7436‘ squares. The desiger here would be wise to change the x in the .435 square
to a 1 and the x in the ABquuare to a 0, since this would produce a quad that can
be looped to produce 2: = A, as shown in Figure 4-18(c).

Whenever don’t-care conditions occur, we must decide which .7: to change to 0
and which to 1 to produce the best K-map looping (i.e., the simplest expression).
This decision is not always an easy one. Several end-of-chapter problems will pro-
vide practice in dealing with don’t-care cases. Here’s another example.

“don't
care"

A
0
0
0
O
1
‘I
l
1

““OO-fi-‘OOQ
dd-‘XXOOON



(8)

FIGURE 4-18 'Don't-care' conditions should be changed to 0 or 1 to produce K-map
looping that yields the simplest expression.



Let’s design a logic circuit that controls an elevator door in a three-story building.
The circuit in Figure 4-1960 has four inputs. M is a logic signal that indicates when
the elevator is moving (M = 1) or stopped (M It 0). F1, F2, and F3 are floor
indicator signals that are normally LOW, and they 30 HIGH only when the elevator
is positioned at the level of that particular floor. For example, when the elevator is
lined up level with the second floor, F2 = l and F1 = F3 = 0. The circuit output
is the OPEN signal which is normally LOW and is to 30 HIGH when the elevator
door is to be opened.