1
198:211
Computer Architecture
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Topics:
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Data representation 2.1 and 2.2 of the book
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Floating point
2.4 of the book
Lecture 8,9
(W5)
Fall 2012
2
Computer Architecture
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What do computers do?
3
Number System
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Comprises of
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Set of numbers or elements
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Operations on them (+
- / *)
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Rules that define properties of operations (identity,
inverse
…
)
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Need to assign value to numbers
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Let us take decimal system
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1
’
s place, 10
’
s place, 100
’
s place etc
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Base 10
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Value=
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Humans use decimal
∑
×
i
i
10
4
Binary numbers
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Base 2; each digit is 0 or 1
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Each bit in place
i
has value 2
i
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Binary representation is used in computers
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Easy to represent by switches (on/off)
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Manipulation by Digital logic in hardware
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But hard for humans to read
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(13)
10
= (1101)
2
5
Hexadecimal representation
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Binary hard to read for humans
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Especially 16 bits, 32 bits, 64 bits
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1010101001010101
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Base 16 representation or hex representation
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Symbols ={0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
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Value =
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First
10 (0 through 9) symbols are same as
decimal numbers
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A=10,B=11,C=12, D=13, E=14, F=15
∑
×
i
i
16
6
Same for Hex
7
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Example: Convert
10 in decimal to binary
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The code
for binary works for any base with modifications
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For
hex, replace by N%16
and N=N/16 replace
reminders > 9 by A, B, C, D, E and F
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Example: Convert 240 to HEX
8
Binary to decimal
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Convert 110110 to decimal
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Value = i*2
i
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Value = 2
5
2
4
2
2
2
1
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= 32+ 16 + 4 + 2
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= 54
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9
Converting Hex to binary
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Each digit in Hex can be represented by 4 bit
binary (base 16) or nibble
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Convert 2A8C to binary
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0010 1010 0100 1100
10
Convert Binary to hex
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Group binary bits into groups of four
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Replace each nibble by a hex digit
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Example 1011011110011100
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1011
0111
1001
1100
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B
7
9
C
or 0x
B
7
9
C
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In C, numeric constants starting with 0x are
interpreted as being in hexadecimal
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Examples
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0x8F7A93 to binary
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1011011110011100 to hex
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0xC4E5 to decimal
