Page 338 - Concise Encyclopedia of Robotics

Truth Table
was originally designed and patented by Lockheed Aircraft. Tri-star wheel
locomotion is applicable to use by remotely controlled robots on the Moon
or on distant planets.
See also ADAPTIVE SUSPENSION VEHICLE, ROBOT LEG, TRACK-DRIVE LOCOMOTION, and
WHEEL-DRIVE LOCOMOTION.
TRUTH TABLE
A truth table is a way of breaking down a logical expression. Truth tables
show outcomes for all possible situations. The table shows an example. It
is arranged in columns, with each column representing some part of the
whole expression.Truth values can be shown by T or F (true or false); often
these are written as 1 and 0.
Truth table: breakdown of a logical statement
X Y Z X + Y – (X + Y)XZ – (X + Y) + XZ
0 0 0 0 1 0 1
0 0 1 0 1 0 1
0 1 0 1 0 0 0
0 1 1 1 0 0 0
1 0 0 1 0 0 0
1 0 1 1 0 1 1
1 1 0 1 0 0 0
1 1 1 1 0 1 1

The left-most columns of the truth table give the combinations of values
for the inputs. This is done by counting upwards in the binary number
system from 0 to the highest possible number. For example, if there are
two variables, X and Y, there are four value combinations: 00, 01, 10, and
11. If there are three variables, X, Y, and Z, there are eight combinations:
000, 001, 010, 011, 100, 101, 110, and 111. If there are n variables, where n
n
is a positive integer, then there exist 2 possible truth combinations.When
there are many variables, a truth table can become gigantic, especially
when the logical expression is complex. Computers are ideal for working
with such tables.
In most truth tables, X AND Y is written XY or X*Y. NOT X is written
with a line or tilde over the quantity, or as a minus sign followed by the
quantity. X OR Y is written X + Y.
The table shows a breakdown of a three-variable expression.All expres-
sions in electronic logic, no matter how complicated, can be mapped in this

