Comp Architecture - Digital
Computer
1
Computer Architecture & Org.
Unit II –
Data And Program
Representation
Bizuayehu Getnet
[email protected]

Comp Architecture - Digital
Computer
2
Outline
Digital Signal
Boolean Algebra
Logic Gates
Combinational Circuits
Sequential Circuits

Digital Logic
Built on two-valued logic system
Can be interpreted as
Five volts and zero volts
High and low
True and false
Comp Architecture - Digital
Computer
3

Data Representation
Comp Architecture - Digital
Computer
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Builds on digital logic
Applies familiar abstractions
Interprets sets of Boolean values as
Numbers
Characters
Addresses

Binary Digit (Bit)
Direct representation of digital logic
values
Assigned mathematical interpretation
0 and 1
Multiple bits used to represent complex
data item
Comp Architecture - Digital
Computer
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Byte
Set of multiple bits
Size depends on computer
Examples of byte sizes
CDC: 6-bit byte
BBN: 10-bit byte
IBM: 8-bit byte
On many computers, smallest addressable unit
of storage
Note: following most modern computers, we will
assume an 8-bit byte
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Computer
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Byte Size And Values
Number of bits per byte determines range
of values that can be stored
Byte of
k bits can store 2
k
values
Examples
Six-bit byte can store 64 possible values
Eight-bit byte can store 256 possible values
Comp Architecture - Digital
Computer
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Binary Representation
0 0 0
0 1 0
1 0 0
1 1
0
0 0 1
0 1 1
1 0 1
1 1
1
All possible combinations of three bits
Comp Architecture - Digital
Computer
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Meaning Of Bits
Bits themselves have no intrinsic meaning
Byte merely stores string of 0’s and 1’s
All interpretation determined by use
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Computer
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Example Of Interpretation
Assume three bits used for status of
peripheral devices
First bit has the value 1 if a disk is connected
Second bit has the value 1 if a printer is
connected
Third
bit has the value 1 if a keyboard is connected
Comp Architecture - Digital
Computer
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Arithmetic Values
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Computer
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Combination of bits interpreted as an integer
Positional representation uses base 2
Note: interpretation must specify order of bits
Example:
0 1 0 1 0 1 is interpreted as:
0 × 2
5
+ 1 × 2
4
+ 0 × 2
3
+ 1 × 2
2
+ 0 × 2
1
+ 1 × 2
0
= 21

Boolean Expression/Function
Comp Architecture - Digital
Computer
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A Boolean Function
An algebraic expression called Boolean
expression which consists of binary variables,
the constants 0 and 1 and the logic operation
symbols

Truth Table Formation
Comp Architecture - Digital
Computer
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A truth table represents a table having all
combinations of inputs and their corresponding
result

Methods to simplify the Boolean
function

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- Fall '19
- Logic gate, Combinational Circuits, Byte of k bits