1. 2.2 General Positional-Number-System Conversion
Binary, octal or hexadecimal to decimal
Examples
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2. 2.2 General Positional-Number-System Conversion
Decimal to binary, octal or hexadecimal
When D is a integer
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3. 2.2 General Positional-Number-System Conversion
Divide D by r
the remainder will be c0. Furthermore, the quotient Q has the same form as the oriental D. Therefore, successive divisions by 2 yield successive digits ci of D from right to left, until all the digits of d have been derived.
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4. 2.2 General Positional-Number-System Conversion
Examples
252=12 remainder 1 c0
2=6 remainder 0 c1
2=3 remainder 0 c2
2=1 remainder 1 c3
2=0 remainder 1 c4
2510=110012
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5. 2.2 General Positional-Number-System Conversion
Simply 8 22 (3
179 2 89 (1
179
(LSB) 8 2 (6 8 (2 2 44 (1 2 22 (0 2 11 (0
17910=2638 2 5 (1 2 (1 16 11 (3
179 1 2 (0 16 (B 2 (1
(MSB)
17910=B316
17910=
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6. 2.2 General Positional-Number-System Conversion
When D is a fraction
Multiply D by r.
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7. 2.2 General Positional-Number-System Conversion
The integer will be c-1. Furthermore, the fraction of the product P has the same form as the oriental D. Therefore, successive multiply by r yield successive digits c-i of D from left to right, until the error is satisfying. .
Examples
0.625
2= integer 1 c-1
2= integer 0 c-2
2= integer 1 c-3
=0.1012
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8. 2.2 General Positional-Number-System Conversion
Converting with six significant digits.
0.7262
0.7268
1) 2
5) 8
0) 2
6) 8
1) 2
3) 8
1) 2
5) 8
1) 2
5) 8 0) 4)  
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9. 2.2 General Positional-Number-System Conversion
Binary to octal or hexadecimal
Examples
= = 43168
= = 8CE16
= =
= = 2.B216
Octal or hexadecimal to binary
Examples
5.678=
3.A516=
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10. 2.2 General Positional-Number-System Conversion
bit, byte, word, and nibble
bit –– one binary digit is called bit.
byte –– 8 binary digits is called byte.
word –– n-bit word means one word has n binary digits.
nibble –– 4-bit or half-byte is called nibble.
Example
A hexadecimal number is 5678ABCD16 .
How many binary digits has it?
How many 8-bit bytes has it?
What is the hexadecimal value of every 8-bit byte?
How many 2-byte words has it?
How many 32-bit words has it?
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11. 2.2 General Positional-Number-System Conversion
Answer
5678ABCD16 =
It has 32 binary digits.
It has four 8-bit bytes.
The hexadecimal values of four 8-bit bytes are 5616, 7816, AB16, CD16.
It has two 2-byte words.
It has one 32-bit word.
A file’s size is 20bytes. How many 1-bit memory units need for saving this file? If a file’s size is 1kbytes?
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