Computer System
"In order to make a computer work, information needs to be converted into a format that can be understood by the computer.”
Understanding a computer’s basic data units such as binary numbers, bits, bytes, words, etc. and their conversions from and to octal, decimal, and hexadecimal digits
Understanding basic concepts of computer internal data representation, focusing on numeric data, character codes etc
Some Terminology
Data representation unit and processing unit
1. Binary Digits (Bits)
Two levels of status in computer’s electronic circuits
Whether the electric current passes through it or not
Whether the voltage is high or low
1 digit of the binary system represented by "1" or "0"
Smallest unit that represents data inside the computer
1 bit can represent 2 values of data, "0" or "1"
2 bits can represent 4 different values
"00", "01", "10", "11"
Bit representation
2. Bytes
A byte is a unit that represents with 8 bits 1 character or number, 1 byte = 8 bits
E.g. "00000000", "00000010", etc.
1 bit can be represented in 2 ways, i.e. combination of 8 bit patterns into 1 byte enables the representation of 28 = 256 types of information
Using a 1-byte word, 256 different characters can be represented – sufficient for most Western character sets
However, the number of kanji (Chinese characters) amounts to thousands of different characters, hence a 1-byte word system is insufficient
Two bytes are connected to obtain 16 bits, 216 = 65,536
A 2-byte word
3. Word
The smallest unit that represents data inside a computer
Increase operation speed
4. Number systems
Binary system is used to simplify the structure of electronic circuits that make up a computer
Hexadecimal number is a numeric value represented by 16 numerals from "0" to "15" to ease the representation of binary numbers for humans – computers are capable of only using binary numbers
Numeric Systems
Also known as Base Systems or Radix Systems
Available digits:
Decimal system (base 10)
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Binary system (base 2)
0, 1
Octal system (base 8)
0, 1, 2, 3, 4, 5, 6, 7
Hexadecimal (base 16)
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
where A=10,B=11,C=12,D=13,E=14,F=15
Addition and subtraction of binary numbers
Addition
0 + 0 = 0 (or 010)
0 + 1 = 1 (or 110)
1 + 0 = 1 (or 110)
1 + 1 = 10 (or 210)
Subtraction
0 – 0 = 0
0 – 1 = -1
1 – 0 = 1
1 – 1 = 0
4. Addition and subtraction of hexadecimal numbers
Addition
Performed starting at the lowest (first from the right) digit
A carry to the upper digit is performed when the result is higher than 16
Subtraction
Performed starting at the lowest (first from the right) digit
A borrow from the upper digit is performed when the result is negative
First column from right
D + 7 = (In the decimal system: 13 + 7 = 20) = 16 (carried 1) + 4
The sum of the first column is 4 and 1 is carried to the second column.
Second column from right
1 + 8 + 1 = (In the decimal system: 10) = A
Carried from the first column
Third column from right
A + B = (In the decimal system: 10 + 11 = 21) = 16 (carried 1) + 5The sum of the third column is 5 and 1 is carried to the fourth column.
The result is (15A4)16.
Hexadecimal Subtraction
First column from right
Since 3 – 4 = –1, a borrow is performed from D in the second digit (D becomes C).
16 (borrowed 1) + 3 – 4 = F (In the decimal system: 19 – 4 = 15)
Second column from right
C – 7 = 5 (In the decimal system: 12 – 7 = 5)
Third column
6 – 1 = 5
The result is (55F)16.
