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

Write short note on quantization, Write short note on Quantization. Qua...

Write short note on Quantization. Quantization: This is the first step in PCM. The whole amplitude range of the modulating signal is divided in a number of standard levels term

Which electro mechanical switch had fewer moving parts, The             el...

The             electro mechanical switch (developed in 1938) had fewer moving parts than earlier switches. (A)  No. 1ESS                                 (B)  Strowger (

Weka uses a gaussian - radial basis function, A data set with 1000 rows is ...

A data set with 1000 rows is input to a neural network in Weka. The test option is set to 10-fold cross validation and the neural network option validationSetSize = 20%. How many r

Managerial benefits, MANAGERIAL BENEFITS Implement integrated relia...

MANAGERIAL BENEFITS Implement integrated reliability engineering and product assurance program in all aspects of the product life-cycle, covering purchase, engineering, R&D

Define syntax of mpi_bcast function, Q. Define syntax of MPI_Bcast function...

Q. Define syntax of MPI_Bcast function? MPI_Bcast(msgaddr, count, datatype, rank, comm):   This function is used by a process ranked rank in group comm to transmit messag

What are conversion routines, What are conversion routines? Non-standa...

What are conversion routines? Non-standard conversions from present format to sap internal format and vice-versa are executed with so known as conversion routines.

Example of prolog, Example of Prolog: We can say that this is also tru...

Example of Prolog: We can say that this is also true if there are four even numbers. Now we have our first rule: • If there are three or four even numbered cards, such play

Explain the random scan and raster scan displays, Define Random scan/Raste...

Define Random scan/Raster scan displays?  Random scan is a method in which the display is made by the electronic beam which is directed only to the points or part of the screen

Overfitted the data, Overfitted the data: Moreover notice that as time...

Overfitted the data: Moreover notice that as time permitting it is worth giving the training algorithm the benefit of the doubt as more as possible. However that is, the error

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