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

Illustrate the advantages of register transfer, Register Transfer We as...

Register Transfer We assign computer registers by capital letters to denote function of the register. Such as, the register which holds an address for memory unit is usually

How did you find web server related issues, Using Web resource monitors we ...

Using Web resource monitors we can search the performance of web servers. Using these monitors we can examine throughput on the web server, number of hits per second that happened

BCD ADDER, create a BCD adder combinational ckt. that adds 2 digit BCD inpu...

create a BCD adder combinational ckt. that adds 2 digit BCD inputs

Describe the hardwired control method, Describe the Hardwired control metho...

Describe the Hardwired control method for generating the control signals Hard-wired control can be explained as sequential logic circuit that generates particular sequences of

What is the function of a data element, What is the function of a data elem...

What is the function of a data element? A data element defines the role played by a domain in a technical context.  A data element having of semantic information.

Word puzzle, You are required to make a class of WordPuzzle, which is basic...

You are required to make a class of WordPuzzle, which is basically a game of finding words inside a 2d-array of characters. The class needs to take rows and columns as arguments an

Distinguish between combinational & sequential logic circuit, Distinguish b...

Distinguish between combinational logic circuits and sequential logic circuits. Ans: Combinational logic circuits:- (i) Outputs only depend upon present state of the i

Forall statement in fortran, Q. FORALL Statement in fortran? The FORALL...

Q. FORALL Statement in fortran? The FORALL statement permits for more common assignments to sections of an array. A FORALL statement has general form.   FORALL ( triplet, ..

What are the major systems of a telecommunication network, What are the maj...

What are the major systems of a telecommunication network? The main systems of any telecommunication network may contain the following main systems: a. Subscriber end instr

Define ufd and mfd, Define UFD and MFD.   In the two-level directory st...

Define UFD and MFD.   In the two-level directory structure, every user has own user file directory (UFD). Every UFD has a same structure, but lists only the files of a single u

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