Lecture 2.ppt - Computer Architecture Org Unit II \u2013 Data And Program Representation Bizuayehu Getnet [email protected] Comp Architecture Digital

# Lecture 2.ppt - Computer Architecture Org Unit II – Data...

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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 4 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 5
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 Comp Architecture - Digital Computer 6
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 7
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 8
Meaning Of Bits Bits themselves have no intrinsic meaning Byte merely stores string of 0’s and 1’s All interpretation determined by use Comp Architecture - Digital Computer 9
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 10
Arithmetic Values Comp Architecture - Digital Computer 11 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 12 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 13 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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• Logic gate, Combinational Circuits,  Byte of k bits

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