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System Architecture Computer words are defined using bits so words are represent

ID: 3716819 • Letter: S

Question

System Architecture

Computer words are defined using bits so words are represents using binary numbers. However, there are many different ways that we can represent numbers such as integers (base 10), octal and hexadecimal numbers. It can however be potentially confusing of how to convert one numeric value to another.

Research various methods of manual conversion of these numbers and share the most optimal method of conversion in your perspective.

Demonstrate how the conversion would work using your method of choice by explaining the steps involved in the conversion.

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Explanation / Answer

Number System

1) Decimal to binary conversion

               ex:-

                     (254)10 is going to convert binary

                1 3 7 15 31 63 127 254   ---->divide 254 by 2 until 1

                1 1 1 1   1     1     1    0       --->put 1 in all odd number place and put 0 in all even number places

                  (254)10=(11111110)2

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2)Octal to binary

              Ex:-

                      (254)8

            Split number into single digits---> 2     5    4

Divide each digit with 2

                   First digit-->     1      2  

Add odd or even binary--->     1     0

Octal representation is 3 digit format , so put 0 before--->010

                 Second digt---->       1    2 5

Add odd or even binary--->          1    0 1

                 third digt---->   1 2 4
Add odd or even binary---> 1 0 0      

Combine together-->010101100

(254)8=(010101100)2

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2)HexaDecimal to binary

              Ex:-

                    (254)16

Split number into single digits---> 2     5    4

Divide each digit with 2

                   First digit-->     1      2  

Add odd or even binary--->     1     0

hex representation is 4 digit format , so put 0 before--->0010

                 Second digt---->       1    2 5

Add odd or even binary--->          1    0 1

hex representation is 4 digit format , so put 0 before--->0101

                 third digt---->   1 2 4
Add odd or even binary---> 1 0 0      

hex representation is 4 digit format , so put 0 before--->0100

Combine together-->001001010100

(254)16=(001001010100)2