Transcript NguyenLeCS147 - presentation

Nguyen Le
CS147
Section overview
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2.4 Signed Integer Representation
2.4.1 – Signed Magnitude
2.4.2 – Complement Systems
2.4.3 – Unsigned Versus Signed Numbers
2.4.4 – Computers, Arithmetic, and Booth’s Algorithm
2.4.5 – Carry Versus Overflow
Unsigned integer representation
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1
0
0
1
1
1
1
1
1
0
1
0
1
 carries
1 1 1 0 0
0 1 0 1 1
0 0 1 1 1
3 methods of representation
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Signed magnitude
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One’s complement
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Two’s complement
Signed magnitude
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Signed magnitude representation includes
a sign as the first bit of the storage
location. A “1” in the high-order bit (or leftmost bit) indicates a negative number and
the rest of the remaining bits represent the
number itself.
Ex: +1 and -1 in an 8-bit word would be
 0 0 0 0 0 0 0 1 (+1)
 1 0 0 0 0 0 0 1 (-1)
Signed magnitude addition
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0
0
0
1
1 0 0
0 1 0
1 1 1
1
1
0
0
1
1
0
0
1
 carries
1 1
1 1
1 0
Overflow
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Overflow in signed numbers occurs when the sign of
the result is incorrect. The sign bit is used only for
the sign, so we can’t carry into it.
1
0
0
0
1
1 0 0
1 1 0
0 1 1
1
1
0
0
1
1
0
0
1
 carries
1 1 (79)
1 1 (99)
1 0 (50)
79 + 99 =/= 50
Signed magnitude subtraction
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0
0
0
0
1 1
1 0
0 0
1
0
0
1
1
0
1
0
2  borrows
0 1 1 (99)
1 1 1 (79)
1 0 0 (20)
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99 – 79 = 20
One’s compliment
Flip the bits for all negative numbers.
The last carry is added to the sum.
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1  1
0
1
0
1
1 1
 carries
0 1 0 1 1 1 (23)
1 1 0 1 1 0 (-9)
0 0 1 1 0 1
+ 1
0 0 0 0 1 1 1 0 (14)
1
0
1
0
Two’s compliment
Flip the bits for all negative numbers.
Add 1.
23 = 00010111
-23 = 11101000 + 1 = 11101001
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0 0 0 0 1 0 0 1 (9)
1 1 1 0 1 0 0 1 (-23)
1 1 1 1 0 0 1 0 (-14)
Section overview
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2.6 Character Codes
2.6.1 – Binary-Coded Decimal
2.6.2 – EBCDIC
2.6.3 – ASCII
2.6.4 – Unicode
Character codes
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We’ve gone over how digital computers use the
binary system to represent and manipulate
numeric values, but have yet to consider how
these internal values can be converted to a form
that is meaningful to humans. This is done through
a coding system used by the computer and how
the values are stored and retrieved.
BCD
Binary Coded Decimal (BCD) is very
common in electronics, particularly those
that display numerical data, such as alarm
clocks and calculators.
 4-bit binary form later extended to 6
 1265 = 0000 0001 0010 0110 0101
1101
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EBCDIC
Extended Binary Coded Decimal
Interchange Code (EBCDIC) used in
IBM mainframe and midrange computer
systems
 8-bit binary form
 1265 = 1111 0001 1111 0010 1111
0110 1101 0101
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ASCII
The American Standard Code for
Information Interchange (ASCII) was
created to better transmit data between
systems.
 Defines codes for 32 control characters,
10 digits, 52 letters (upper and lowercase), 32 special characters, and more.
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Unicode
16-bit base coding with the capacity to
encode the majority of characters used
in every language of the world.
 Unicode also defines an extension
mechanism that will allow for the coding
of an additional million characters.
 Default character set of the Java
programming language.
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