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1. Data in the Computer
- mostly from “Irv Englander, The Architecture of Computer Hardware
and Systems Software – An Information Technology Approach, 2nd ed.,
Wiley 2000”.
1.1 Computer Data Unit
- Computers perform all their operations using the binary number system (이진
법) using base 2. Calculations are performed using binary arithmetic(이진수학).
Range: How many different numbers can be represented by digits.
The range of K digit in base B is
R = Bk
1 bit : (R=21, 0 and 1)
8 bit = 1 Byte (R=28=256)
10 bit: R=1024 (=1K)
16 bit = 2 Byte (half word, R=65,536 = 64K)
20 bit: (R=1,048,576 = 1M)
32 bit = 4 Byte (word, R=4,294,967,296 = 4G)
64 bit = 8 Byte (double word, R = approx. 1.6x1019 )
1Kilo (K) = 210 = 1024 Byte
1Mega (M) = 220
1Giga (G) = 230
1Tera (T) = 240
1.2 Counting in Different Bases
527 = 5x102 + 2x101 + 7x100
6248=6x82+2x81+4x80
= 6x64 + 2x8 + 4 = 40410
* No subscript at numbers of base 10.
1110012+10101112 =
11011012 x 1001102 =
1.3 Numeric Conversion between Number Bases
Base 10 to another base:
5)
6124
5)
1224 - 4
5)
244 - 4
5)
48
-4
5)
9
-3
5)
1
-4
6124 = 1434445
6124 = (
)8
6124 = (
)16
Another number base to base 10:
137548
1
x8
8 + 3 = 11
x 8
88 + 7 = 95
x8
760 + 5 = 765
x8
6120 + 4 = 612410
1.4 Hexadecimal Numbers and Arithmetic
Octal: 0, 1, 2, 3, 4, 5, 6, 7
Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
2A4F16 =
Special Conversion Case: 2, 8, 16 -> Grouping
11010111011000
0011 0101 1101 1000
= 35D816
011 010 111 011 000
= 327308
Computers prefer to use hexadecimal
1 bit = binary
8 bit = two hexadecimal numbers (8A)
--- 1 Byte
16bit = four hexadecimal numbers (A3 FD)
32bit = eight hexadecimal numbers (E8 12 D0 2F, internet address)
64bit = sixteen hexadecimal numbers
(00 C0 26 5B F7 2B, Ethernet Card Address)
(Exercise) Find out the IP Address of your computer and convert it into
Hexadecimal.
1.5 Fractions
1/10 = 0.110 exactly.
= 0.000110110112…… endless with repeat cycle of four
1/3 = 0.33333333… endless with repeat cycle of one
= 0.13 exactly.
0.258910 = 2 x (10-1) + 5 x (10-2) + 8 x (10-3) + 9 x (10-4)
0.10112 = 1 x (2-1) + 0 x (2-2) + 1 x (2-3) + 1 x (2-4) = 0.6875
-> Fractions in base 2 can always be converted exactly to fractions in
base 10.
Another method of fraction conversion, From another base to base 10:
0.32 = 32 x 10-2. Similarly,
0.10112 = 10112 x 2-4
= 11 / 16 = 0.6875
(example) convert 0.122013 to base 10 with two methods.
(example) convert 0.1100112 to base 10 with the simpler method you
prefer.
Convert 0.82812510 to base 2.
0.828125
x
2
1.656250
x
The 1 is saved as result, then dropped.
2
1.312500
x
2
0.625000
x
2
1.125000
x
2
0.500000
x
2
1.000000
reading downward -> 0.1101012
Special fraction conversion between base 2, 8, 16 by grouping:
0.101112
= 0.101 1102
= 0.568
0.101112 = 0.1011 10002
= 0.B816
1.6 Computer Data Type
Boolean: True or False, 1bit
Char: Character data (ASCII), 8bit or 1byte
Integer: positive or negative whole numbers
8bit Unsigned Integer : 0 ~ 255 (Most optical Images)
8bit Signed Integer: -128 ~ 127
16bit Unsigned Integer: 0 ~ 65535 (SAR SLC)
16bit Signed Integer: -37268 ~ 37267
32bit Unsigned Integer: 0 ~ 4,294,967,295
32bit signed integer
Real: numbers with decimal portion.
32bit (4byte) real
64bit (8byte) double
1.7 Image Data
Data Type:
Pixel Numbers:
Rows and columns (integers)
Band Type:
BIL (Band Interleaved by Line)
BIP (Band Interleaved by Pixel)
BSQ (Band Sequential)
<< Exercise >>
1. 1011011012 + 100110112
2. 2AB3 + 35DC
3. Multiply 11012 x 1012
4. convert binary to octal and hexadecimal
A. 10111010101010
B. 1101010
C. 0.001001100