Page 96 - Understanding Automotive Electronics

2735 | CH 3 Page 83 Tuesday, March 10, 1998 11:03 AM

ELECTRONICS FUNDAMENTALS 3

Converting from decimal to binary can be accomplished by finding the
largest number that is a power of 2 (divisor) that will divide into the decimal
number (dividend) with a 1 as a quotient, putting a 1 in its place, and
subtracting the divisor (the number used to divide with) from the decimal
number (dividend) to get a remainder. The operation is repeated by dividing
with the next lower number that is a power of 2 until the binary ones’ place has
been tested. Any time the dividend is less than the divisor, a 0 is put in that
place and the next power of 2 divisor is tried. For instance, to find the binary
equivalent for the decimal number 73, the largest number that is a power of 2
6
and that will divide into 73 with a quotient of 1 is 64 (2 ):
(2 ) 73/64 = 1 remainder (73 – 64) = 9
6
5
(2 ) 9/34 = 0
4
(2 ) 9/16 = 0
3
(2 ) 9/8 = 1 remainder (9 – 8) = 1
2
(2 ) 1/4 = 0
(2 ) 1/2 = 0
1
0
(2 ) 1/1 = 1
Therefore,
73 = 1001001
LOGIC CIRCUITS (COMBINATORIAL)
Digital computers can perform binary digit (bit) manipulations very
easily by using three basic logic circuits or gates: the NOT gate, the AND gate,
and the OR gate. Digital gates operate on logical variables that can have one of
two possible values (e.g., true/false, saturation/cutoff, or 1/0). As was previously
explained, numerical values are represented by combinations of 0 or 1 in a
binary number system.
As mentioned earlier, digital circuits operate with transistors in one of two
possible states—saturation or cutoff. Since these two states can be used to
represent the binary numbers 1 or 0, combinations of transistors that are in one
of these two states can be used to represent multiple-digit binary numbers. The
input and output voltages for such digital circuits will be either “high’’ or “low,’’
corresponding to 1 or 0. High voltage means that the voltage exceeds a high
threshold value that is denoted V . Symbolically, the high-voltage condition
H
corresponding to logical 1 is written
V > V H
meaning V exceeds V . Similarly, low voltage means that voltage V is given by
H
V < V L

meaning V is less than V , where V denotes the low threshold value. The actual
L
L
values for V and V depend on the technology for implementing the circuit.
H
L
Typical values are V = 2.4 volts and V = 0.8 volt.
L
H
UNDERSTANDING AUTOMOTIVE ELECTRONICS 83