Morgan Kaufmann Publishers
24 February, 2015
Chapter 3
—
Arithmetic for Computers
1
C
OMPUTER
O
RGANıZATıON
AND
D
ESıGN
The Hardware/Software Interface
5
th
Edition
Chapter 3
Arithmetic for Computers
Chapter 3
—
Arithmetic for Computers
—
2
Arithmetic for Computers
Operations on integers
Addition and subtraction
Multiplication and division
Dealing with overflow
Floating-point real numbers
Representation and operations
§
3.1 Introduction
Sign
One's
Two's
Magnitude
Complement
Complement
000 = +0
000 = +0
000 = +0
001 = +1
001 = +1
001 = +1
010 = +2
010 = +2
010 = +2
011 = +3
011 = +3
011 = +3
100 = -0
100 = -3
100 = -4
101 = -1
101 = -2
101 = -3
110 = -2
110 = -1
110 = -2
111 = -3
111 = -0
111 = -1
Issues:
balance, number of zeros, ease of
operations
Two`s Complement is used.
Possible Representations
Negating a two's complement number:
invert all bits and
add 1
(“negate” and “invert” are quite different!)
Converting n bit numbers into numbers with more than n
bits:
MIPS 16 bit immediate gets converted to 32 bits for
arithmetic
copy the most significant bit (the sign bit) into the
other bits
:
0010
-> 0000 0010
1010
-> 1111 1010
"sign extension"
(lbu
vs.
lb)
Two's Complement Operations

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