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计算机组成原理英文版课件:3-DataRepresentation.pdf
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计算机组成原理英文版课件:3-DataRepresentation.pdf
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Kai Huang
Data Representation
3/14/2014 Kai.Huang@SYSU 2
The First Chinese ASPLOS Best Paper
19
th
International Conference on
Architectural Support for Programming
Languages and Operating Systems
3/14/2014 Kai.Huang@SYSU 3
Positional Number Systems
Binary and Hexadecimal Numbers
Base Conversions
Integer Storage Sizes
Binary and Hexadecimal Addition
Signed Integers and 2's Complement Notation
Sign Extension
Binary and Hexadecimal subtraction
Carry and Overflow
Character Storage
Outline
3/14/2014 Kai.Huang@SYSU 4
Different Representations of Natural Numbers
XXVII Roman numerals (not positional)
27 Radix-10 or decimal number (positional)
11011
2
Radix-2 or binary number (also positional)
Fixed-radix positional representation with k digits
Number N in radix r = (d
k–1
d
k–2
. . . d
1
d
0
)
r
Value = d
k–1
×r
k–1
+ d
k–2
×r
k–2
+ … + d
1
×r + d
0
Examples: (11011)
2
= 1×2
4
+ 1×2
3
+ 0×2
2
+ 1×2 + 1 = 27
(2103)
4
= 2×4
3
+ 1×4
2
+ 0×4 + 3 = 147
Positional Number Systems
3/14/2014 Kai.Huang@SYSU 5
Each binary digit (called bit) is either 1 or 0
Bits have no inherent meaning, can represent
o Unsigned and signed integers
o Characters
o Floating-point numbers
o Images, sound, etc.
Bit Numbering
o Least significant bit (LSB) is rightmost (bit 0)
o Most significant bit (MSB) is leftmost (bit 7 in an 8-bit number)
Binary Numbers
1 0 0 1 1 1 0 1
2
7
2
6
2
5
2
4
2
3
2
2
2
1
2
0
0 1 2 3 4 5 6 7
Most
Significant Bit
Least
Significant Bit
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