Page 99 - Understanding Automotive Electronics

2735 | CH 3 Page 86 Tuesday, March 10, 1998 11:03 AM

3 ELECTRONICS FUNDAMENTALS

truth table outputs for the NAND and NOR gates are the reverse of those for
the AND and OR gates, respectively. Where C was 1, it is now 0 and vice versa.
All of these gates are available in integrated circuit form with various quantities
of gates in a package and various numbers of inputs per gate.

XOR and Adder Circuits

XOR gates, which out- Another complex gate performs the exclusive OR function, abbreviated as
put a high only when XOR, illustrated in Figure 3.7a. The output is high only when one input is
one or the other input is high, but not when both are high. This gate very commonly is used for
high, are commonly comparison of two binary numbers because if both inputs are the same, the
used to add binary num- output is zero. The equivalent combination of basic gates to perform this
bers. function is shown in Figure 3.7a. The XOR gate is also available in an integral
package so it is not necessary for the designer to interconnect separate gates in
this manner to build the function.
All of these gates can be used to build digital circuits that perform all of
the arithmetic functions of a calculator. Table 3.3 shows the addition of two
binary bits in all the combinations that can occur. Note that in the case of
adding a 1 to a 1, the sum is 0, and a 1, called a carry, is placed in the next place
value so that it is added with any bits in that place value. A digital circuit
designed to perform the addition of two binary bits is called a half adder and is
shown in Figure 3.7b. It produces the sum and any necessary carry, as shown in
the truth table.
A half adder circuit does not have an input to accept a carry from a
previous place value. A circuit that does is called a full adder (Figure 3.7c). A
series of full adder circuits can be combined to add binary numbers with as
many digits as desired. A simple electronic calculator performs all arithmetic
operations using full adder circuits and a few additional logic circuits. In such
circuits, subtraction is performed as a modified form of addition by using some
of the additional logic circuits. Multiplication is accomplished by repeated
addition, and division is accomplished by repeated subtraction.
Of course, the addition of pairs of 1-bit numbers has no major application
in digital computers. On the other hand, the addition of multiple-bit numbers

Table 3.3
Addition of Binary
Bits
Bit A 0 0 1 1
Bit B 0 1 0 1
Sum 0 1 1 10

86 UNDERSTANDING AUTOMOTIVE ELECTRONICS