Service manual

STP 11-25R13-SM-TG
Q - 4
(1) Using the decimal system in electronics would be quite difficult and elaborate because for a
circuit to count there would have to be 10 distinct level changes to represent the 10 distinct symbols. A
new system of counting must be used with digital circuitry and that is the binary number system.
(2) In a binary number system, there are only two symbols used (0 and 1). These can be
represented with electrical signals rather easily. A low voltage level could represent a 0 and a high
voltage level a 1. In some cases, it could be the other way around. All that is needed of the electronic
circuitry is the ability to detect two level changes, a low to a high and a high to a low.
(3) As it is with the decimal system, there are certain math operations that can be performed with
the binary number system. These are conjunction, disjunction, and negation. It must be understood at
this point in our discussion that operations in one number system cannot be used in another number
system. There are certain postulate theorems, laws, and identities, which apply to each number system
independent of any other system.
c. Combination Logic
. Most electronic equipment consists of two types of logic circuits:
combination and sequential.
(1) In a combination logic circuit, the output depends on the state of the inputs when the output is
observed. A sequential logic circuit has memory so its output not only depends on the inputs but also
what the previous inputs were prior to the time at which the output is observed.
(2) Combination logic circuits have the ability to make decisions. Understanding this decision-
making process requires a knowledge of Boolean algebra. Boolean algebra is the mathematics that is
used in performing calculations involving the binary number system. As previously mentioned, the first
operation in this system is conjunction.
d. Conjunction
. Conjunction is defined as follows: C is true only when A and B are simultaneously
true (true = 1 and false = 0).
(1) The symbol for conjunction is (•), so the logic function above can be written as "A • B = C" or
"AB = C" and is read as "A AND B is equal to C". An AND gate is the logic circuit that performs the
mathematical operation of conjunction. All possible combinations for the conjunction operation are in
Table Q-2.
Table Q-2. Combinations for Conjunction
(2) There are no other possibilities in the above table because there are only two symbols used in
the binary system (0 and 1).
e. Disjunction
. The second operation in our new mathematical system is called disjunction and is
defined as follows: C is true if A is true or B is true, or if both A and B are true at the same time.
A • B = C
A B C
0 0 0
0 1 0
1 0 0
1 1 1