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

External report cannot be called, When calling an external report the param...

When calling an external report the parameters or select-options specified in the external report cannot be called.

How is an instruction represented, Q. How is an instruction represented? ...

Q. How is an instruction represented? Instruction is signified as a sequence of bits. A layout of an instruction is called as instruction format. Instruction formats are princi

Explain fixed point representation, Q. Explain Fixed Point Representation? ...

Q. Explain Fixed Point Representation? The fixed-point numbers in binary has a sign bit. A positive number has a sign bit 0 whereas negative number has a sign bit 1. In fixed-p

Explain naming convention in arrays, Explanation Arrays in many programm...

Explanation Arrays in many programming-languages generally show a fixed list of values (e.g. a list of lastnames). Though within SQABasic the size for an array can either be fix

Compute physical address of data byte, Q. Compute Physical address of data ...

Q. Compute Physical address of data byte? Offset of data byte = 0020h Value of data segment register (DS) = 3000h Physical address of data byte   This computation

Acting rationally - artificial intelligence, Acting Rationally: "Al" C...

Acting Rationally: "Al" Capone was finally convicted for tax evasion. Were the police reacting on rationally?? To solve this puzzle, we must first look at how the performance

Liquid crystal displays, LCDs are the screens of choice for lightweight scr...

LCDs are the screens of choice for lightweight screens andportable computers. They consume very little electricity and have advanced technically to quite good resolutions and colou

What is the function of alu, What is the function of ALU? Most of the c...

What is the function of ALU? Most of the computer operations (arithmetic and logic) are performed in ALU. The data needed for the operation is brought by the processor and the

Explain real time operating system, Explain Real Time Operating System? ...

Explain Real Time Operating System? Real time operating System: A real-time operating system has suitably-defined, fixed time constraints. Processing should be done in the d

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

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