Number system, Computer Engineering

Assignment Help:

 

Number systems

 

Consider a decimal number:               7654.32

 

Short hand for:            7 * 103 + 6*102 + 5* 101 + 4*100 + 3*10-1 + 2*10-2

 

Likewise binary number:                     1011.011

 

In full:                         1*23 + 0*22 + 1* 21 + 1*20 + 0* 2-1 + 1* 2-2 + 1*2-3

 

In general the number:                        x­2 x1 x0 . x-1 x-2 x-3

 

In base B is equal to:   x­ B2 + x1  B1 + x B0 + x-1  B-1 + x-2  B-2 + x-3 B-3

 

 

Conversion table.

 

Decimal (Base 10)

Binary (Base 2)

Octal (Base 8)

Hexadecimal (Base 16)

0

0000

00

0

1

0001

01

1

2

0010

02

2

3

0011

03

3

4

0100

04

4

5

0101

05

5

6

0110

06

6

7

0111

07

7

8

1000

10

8

9

1001

11

9

10

1010

12

A

11

1011

13

B

12

1100

14

C

13

1101

15

D

14

1110

16

E

15

1111

17

F

 

 

 

Convert decimal to binary by repeated division by two.

 

 e.g. 2510 in binary?

 

25

  2  =

12

remainder 1

12

  2  =

6

remainder 0

6

  2  =

3

remainder 0

3

  2  =

1

remainder 1

1

  2  =

0

remainder 1

 

Read remainders from bottom up.

Convert decimals less than one to binary by repeated multiplication by two.

 

 e.g. 0.62510 in binary?

 

0.625

  2  =

1.25

whole number 1

0.25

  2  =

0.5

whole number 0

0.5

  2  =

1.0

whole number 1

 

Read whole numbers from top down.

 

Therefore 25.62510 = 11001.1012

 


Related Discussions:- Number system

Why pic18f452 was used in the project designed, I have used the PIC18F452 m...

I have used the PIC18F452 microcontroller for both the main micro and the interface chip device because of it enhanced features that can be used to meet the specification required

Corrosion, Explain the mechanidm of the rusting of iron on the basis of ele...

Explain the mechanidm of the rusting of iron on the basis of electrochemical corrosion?

Which transistor is used in every cell of eprom, Floating gate Avalanche In...

Floating gate Avalanche Injection MOS (FAMOS) transistor is used in every cell of EPROM.

Why process scheduling algorithm favour i/o bound processes, Suppose that a...

Suppose that a process scheduling algorithm favors those processes that have used the least processor time in the recent past. Why will this algorithm favour I/O- bound processes,

Three firm capabilities that are performance in e-commerce, Three firm capa...

Three firm capabilities that are critical for superior firm performance in e-commerce are:- 1.  Information technology capability,  2.  Strategic flexibility, and  3.  Tr

Implementation of BUS, Q. Implementation of BUS Construction of a bus s...

Q. Implementation of BUS Construction of a bus system for four registers employing 4×1 multiplexers is displayed below. Every register has four bits which are numbered 0 throug

What is ram bus technology, What is RAM Bus technology? The key feature...

What is RAM Bus technology? The key feature of RAM bus technology is a fast signalling method used to transfer information among chips. Instead of using signals that have volta

What do you mean by memory mapped i/o, What do you mean by memory mapped I/...

What do you mean by memory mapped I/O? In Memory mapped I/O, there is no particular input or output instructions. The CPU can manipulate I/O data residing in interface register

Dbms, aggregation in dbms?

aggregation in dbms?

Write the command to show the ip host table, show hosts is the command whi...

show hosts is the command which display the IP host table

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd