Page 186 -

243_MasterPieces_04a.qxd 4/18/03 7:05 PM Page 158

158 Masterpiece 4 • PneumADDic II

Binary addition is similar to decimal addition in that you start at the ones place, and
work your way higher places carrying as needed, until you run out of numbers to add.
For example, we want to add decimal 5 to decimal 7 as described in Figure 1.6

Figure 1.6 Binary Addition

Binary Decimal
101 (5)
+111 (7)
----------
Binary Decimal Explanation
111 Carries
101 (5) Value 1
+ 111 (7) Value 2

----------
1100 = (8 * 1 + 4 * 1 + 2 * 0 + 1 * 0 = 12)

In each column, you need to be able to add three binary digits (often referred to as
bits); a bit from Value 1, a bit from Value 2, and the Carry from the previous column.Table
1.2 shows all possible combinations of the three bits and the Sum and Carry.You can use
Table 1.2 to perform the binary addition for each binary place column in Figure 1.4

Table 1.2 Computing the Sum and the Carry

Inputs Outputs
Carry Value 1 Value 2 Carry Sum

0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1

Boolean Logic

A British mathematician named George Boole invented a branch of mathematics which
became known as Boolean logic. Boolean logic deals with two valued number systems
(binary), and defines a simple set of rules of Boolean computation. Boole defined three