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Computer Arithmetic Operations
1. COMPUTER ARCHITECTURE
UNIT – II ARITHMETIC OPERATIONS
CA PPT5 ARITHMETIC, ALU
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ALU - Addition and subtraction – Multiplication – Division – Floating
Point operations – Subword parallelism
2. Arithmetic for Computers
ALU - Arithmetic & Logic Unit
Responsible for performing arithmetic operations such as addition,
subtraction, division and multiplication and logical operations such
as AND, OR and their inversion etc.,
Arithmetic operations are performed on data type
Fixed point numbers
Floating point numbers
Representing number in such data type is known as
Fixed point representation
Floating point representation
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3. Fixed point representation
Integer numbers
2 forms
Signed integer (Negative number) -15
Unsigned integer (Positive number) 15
Techniques used to represent integer numbers are
Signed Magnitude representation
1’s Complement
2’s Complement
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4. Signed Magnitude representation
There are many schemes for representing negative integers with
patterns of bits.
One scheme is sign-magnitude
It uses one bit (MSB) to indicate the sign.
"0" indicates a positive integer, and "1" indicates a negative integer
The rest of the bits are used for the magnitude of the number
Example: -2410 is represented as
1001 1000
The sign "1" means negative
The magnitude is 24 (in 7-bit binary)
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5. Example
Decimal values of the following 8-bit sign-magnitude numbers
10000011 = -3
00000101 = +5
11111111 = ?
01111111 = ?
Represent the following in 8-bit sign-magnitude
-15 = 10001111
+7 = 00000111
-1 = ?
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6. One’s Complement
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Perform NOT operation
Example find 1’s complement for 110101002
9. Addition & Subtraction
Addition
Rules for Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, and carry 1 to the next more significant bit
Example : Add 610 to 710 in binary
11
0110 (610)
+ 0111 (710)
------
1101 (1310)
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10. Addition
Logic circuit which perform addition of 2 bits is call half adder
3 bits (2 significant bit & 1 Carry) is called full adder
Half Adder
Block Diagram Truth Table
i/p
o/p
CA PPT5 ARITHMETIC, ALU
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Half
Adder
A B
S
C
A B S(um) C(arry)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
11. Karnaugh Map
Sum = A B ̅ + A ̅ B. Carry = AB
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A
B
Sum
Carry
Logic Diagram
12. Full Adder
Block Diagram Truth Table
CA PPT5 ARITHMETIC, ALU
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Full
Adder
A B
S
Cout
Carry In
(Cin)
Cin A B S(um) Cout
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
13. Karnaugh Map
S = A ̅ B ̅ Cin + A ̅ BC ̅ in + ABCin Cout = AB + ACin + BCin
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17. Example – Subtraction (Base on MIPS)
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Subtracting 6ten from 7ten can be done directly:
18. Binary Subtraction
Suppose we want to perform A-B
Steps:
Take 2’s Complement of B
Result A + 2’s Complement of B
If Carry is generated Result is Positive (Ignore Carry)
If no Carry Result is Negative & in the 2’s Complement form
Example : Perform (28)10 – (15)10 using 6 bit 2’s Complement
representation
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19. Multiplication
Multiplying 1000ten by 1001ten:
The first operand is called the multiplicand
the second the multiplier
The final result is called the product
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20. First version of the multiplication
hardware
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21. Refined version of the multiplication
hardware
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