7-1
Basic theory
7-1-1 Discrete mathematics
The information managed by computers bears a close relationship with
“discrete mathematics,” which deals with factors such as digital quantity.
Discrete mathematics forms the basis of a wide number of fields, encompassing computer logic circuitry, data structures, and linguistic theory.
1
Numbers and expression
All internal computer commands and data are expressed using binary numbers. An understanding of the fundamental logic behind the binary numbers that form the basis of data expression, as well as other types of
number systems, is essential in order to perform tasks such as programming.
(1)Binary numbers, octal numbers, decimal numbers, hexadecimal numbers
A computer is capable of internally recognizing and processing data based
on the transmission of electric current, voltage fluctuation, and other factors. Data recognized through such means is expressed as values featuring
a combination of the symbols “0” and “1.” This method is known as a
“binary number system.”
However, since it only deals with “0” and “1” arrangements, it is difficult
for humans to utilize such a system. For this reason, information can also
be expressed by replacing this method with a “decimal number system,”
which consists of ten commonly used numerals (“0” to “9”). In addition,
an “octal number system” employing numerals from “0” to “7” and a
“hexadecimal number system,” which is comprised of the numerals “0”
to “9” and alphabet letters from “A” to “F” can be utilized as well.
HexaHexaBinary Decimal Octal
Binary Decimal Octal
decimal
decimal
number number number
number number number
number
number
0
0
0
0
1001
9
11
9
1
1
1
1
1010
10
12
A
10
2
2
2
1011
11
13
B
11
3
3
3
1100
12
14
C
100
4
4
4
1101
13
15
D
101
5
5
5
1110
14
16
E
110
6
6
6
1111
15
17
F
10000
16
20
10
111
7
7
7
1000
8
10
8
* In a hexadecimal number system, “10” through “15” are expressed using “A” to
“F.”
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