Page 185 -

243_MasterPieces_04a.qxd 4/18/03 7:05 PM Page 157

PneumADDic II • Masterpiece 4 157

In Figure 1.4 you can see that switch is flipped to the right, which means the pressure
is forced from the left switch port and sent into the base of the piston, forcing the piston
to expand.
In Figure 1.5 you can see that the switch is flipped to the left, which means the pres-
sure is forced from right port of the switch and sent into the top inlet on the piston,
forcing the piston to contract.

Figure 1.5 A Pneumatic Circuit with a Contracted Piston

Digital Computing

The computers and calculators that we use in our everyday lives compute and calculate
using binary arithmetic. In the decimal arithmetic that we learned in school, a given dec-
imal place can have one of ten possible values, 0 through 9. In binary arithmetic, a given
binary place can have one of two values: 0 or 1.
In decimal mathematics, when we count up from 0, we go through the values, 0, 1, 2,
3, 4, 5, 6, 7, 8, 9, until we’ve used all the possible values, at which point we need to add 1
to the tens place and start over at zero in the ones place (the jump from 9 to 10). Once
we’ve exhausted all values of the ones and tens places, we need to expand up into the
hundreds place (the jump from 99 to 100).
In binary mathematics, instead of having ones, tens, and hundreds places, we have
binary places, 1, 2, 4, 8, where each new place represents two times the value of the pre-
vious place. We can convert the decimal numbers we are familiar with to binary as shown
in Table 1.1.

Table 1.1 Explanation of Decimal to Binary Conversion

Decimal Binary Explanation

0 0
1 01 1 * 1 = 1
2 10 2 * 1 + 1 * 0 = 2
3 11 2 * 1 + 1 * 1 = 3
4 100 4 * 1 + 2 * 0 + 1 * 0 = 4
5 101 4 * 1 + 2 * 0 + 1 * 1 = 5