Number System

Number System
The number system of a number is determined by the Radix of a number.Radix means the base of the number which is obtained by the number of symbols present in that number System.They are as follow:-
 

Sr.No.	Number System	Radix	Symbols
1.	Binary number System	2	0,1
2.	Octal Number System	8	0,1,2,3,4,5,6,7
3.	Decimal Number System	10	0,1,2,3,4,5,6,7,8,9
4.	Hexadecimal Number System	16	0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

1.Binary Number System:- The number System with Radix 2 are said to be binary numbers.It contains only 2 symbols 0 and 1.For Examples (1110)₂,(1001)₂,(1101)₂,(1010)₂,(1010.111)₂,etc.
2.Octal Number System:- The number System with Radix 8 are said to be octal numbers.It contains 8 symbols 0,1,2,3,4,5,6 and 7.For Examples (257)₂,(346)₈,(412)₈,(728)₈,(72.39)₈,etc.
3.Decimal Number System:- The number System with Radix 10 are said to be decimal numbers.It contains 10 symbols 0,1,2,3,4,5,6,7,8 and 9.For Examples (123)₁₀,(786)₁₀,(157)₁₀,(928)₁₀,(28.625)₁₀,etc.
4.Hexadecimal Number System:- The number System with Radix 16 are said to be hexadecimal numbers.It contains only 16 symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.Here A represent for number 10,B represents for number 11,C represents for number 12,D represents for number 13,E represents for number 14,F represents for number 15,For Examples (1ABC)₁₆,(25DE)₁₆,(85C.3D)₁₆,(0AB)₁₆,etc.
Note that for hexadecimal number should start with symbols of numbers only that is 0,1,2,3,4,5,6,7,8,9 and not with A,B,C,D,E,F .If there is a possibility of number to star with alphabets then write 0(zero before that number example (0AB)₁₆,(0ADE)_16,etc.

Conversion of numbers Systems:
# Convert Binary to Decimal:- To convert the binary number into decimal we have to multiply each binary number with 2 and then take the raise to power from Least Significant Bit (LSB) side starting with 0 and so on.
1.(1010)₂   = 1*2³ + 0*2²+ 1*2¹ + 0*2⁰
                  = 1*8 + 0*4 +1*2 + 0*1
                  = 8 + 0 + 2 + 0
                  =(10)₁₀
2.(101)₂    = 1*2² + 0*2¹ + 1*2⁰
                 = 1*4 + 0*2 + 1*1
                 =  4 + 0 +1
                 = (5)₁₀
3.(1001)₂   = 1*2³ + 0*2²+ 0*2¹ + 1*2⁰
                  = 1*8 + 0*4 +0*2 + 1*1
                  = 8 + 0 + 0 +1
                  =(9)_10
4..(1111)₂   = 1*2³ + 1*2²+ 1*2¹ + 1*2⁰
                  = 1*8 + 1*4 +1*2 + 1*1
                  = 8 + 4 + 2 +1
                  =(15)₁₀
But for fractional numbers that is for the numbers with decimal point we have to multiply fractional numbers with 2 raise to power of -1 from decimal point.
1. (1111.101) =1*2³ + 1*2²+ 1*2¹ + 1*2⁰ + 1*2^-1+ 0*2^-2 + 1*2^-3
                      = 1*8 + 1*4 + 1*2 + 1*1+ 1*1/2¹+ 0*1/2² + 1*1/2²
                      = 1*8 + 1*4 + 1*2 + 1*1+ 1*1/2 + 0*1/4 + 1*1/8
                      = 1*8 + 1*4 +1*2 + 1*1+1*0.5 + 0*0.25 + 1*0.125
                      = 8 + 4 + 2 + 1 + 0.5 + 0 + 0.125
                      =(15.625)₁₀
# Convert Decimal to Binary :- To convert the decimal number to binary divide the number by 2 to get integers note down the remainders in front of them simultaneously and then write remainders in reverse order from bottom to top.
  1.(157)₁₀
Solution : -

2	157	Remainders
2	78	1
2	39	0
2	19	1
2	9	1
2	4	1
2	2	0
2	1	1
	0	1

Answer=(11011101)₂

2.(9)₁₀
Solution : -

2	9	Remainders
2	4	1
2	2	0
2	1	0
	0	1

Answer=(1001)₂
Note:Binary counting can be done by taking only those values of numbers from similarly like starting from decimal numbers only those numbers which contains symbols 0 and 1.That is 0,1,2,3,4,5,6,7,8,9,10,11,12,13,............,99,100,101,102,103,....,110,111,...and so on.Cancel the numbers that contains symbols other than 0 and 1.So the counting will be:

Decimal Numbers	Binary numbers	Hexadecimal Numbers
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
6	110	6
7	111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F

# Convert octal to decimal:- To convert the octal number into decimal we have to multiply each octal  number with 8 and then take the raise to power from Least Significant Bit (LSB) side starting with 0 for integers and so on.

1. (157)₈ = 1*8² + 5*8¹ + 7*8⁰
              = 1*64 + 5*40 + 7*1
              = 64 + 200 +7
              = (271)₁₀
2.(459)₈ = 4*8² + 5* 8¹ + 9*8⁰
              = 4*64+5*8+9*1
              =256 + 40 +9
              =(305)₁₀
 But for fractional numbers that is for the numbers with decimal point we have to multiply fractional numbers with 8 raise to power of -1 from decimal point and so on -2,-3,.. .
 1.(351.123)₈   =  3*8² + 5*8¹ + 1*8⁰ + 1*8^-1 + 2*8^-2 + 3*8^-3
                        =  3*64 + 5*8 + 1*1 + 1*1/8¹ + 2*1/8² + 3*1/8³
                        =3*64 + 5*8 + 1*1 + 1*1/8 + 2* 1/64 + 3* 1/512
                        =192 + 40 + 1 + 1*0.125 + 2*0.015625 + 3* 0.001953125
                        = 192 + 40 + 1 + 0.125 + 0.03125 +  0.005859375
                        = (233.162109375)₁₀
# Convert decimal to octal:- To convert the decimal number to octal divide the number by 8 to get integers note down the remainders in front of them simultaneously and then write remainders in reverse order from bottom to top.
1.(157)₁₀
Solution : -

8	157	Remainders
8	19	5
8	2	3
	0	2

Answer=(532)₈

1.(304)₁₀
Solution : -

8	304	Remainders
8	38	0
8	4	6
	0	4

Answer=(064)₈

Visual Basic Examples

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Program 1:- To create Visual Basic application to find the area of rectangle.

Code:-
 Private Sub Command1_Click() Text3.Text = Text1.Text * Text2.Text End Sub

Private Sub Command2_Click()

Text1.Text = " " Text2.Text = " " Text3.Text = " " End Sub


/*************************Output**************************/

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Program 2:- To create Visual Basic application to average of 3 numbers.
Design Window:-

Code:-

Private Sub Command1_Click()

Text4.Text = Str((Val(Text1.Text) + Val(Text2.Text) + Val(Text3.Text)) / 3)

End Sub

Private Sub Command2_Click()

Text1.Text = " "

Text2.Text = " "

Text3.Text = " "

Text4.Text = " "

End Sub

Private Sub Command3_Click()

Unload Me

End Sub


/*************************Output**************************/

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Program 3: To create Visual Basic application to illustrate Date-Time functions.

Code:-

Private Sub Command1_Click ()

Text1.Text = Date

Text2.Text = Time ()

Text3.Text = Year (Date)

Text4.Text = Month (Date)

End Sub

/*************************Output**************************/

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Program 4:-To create Visual Basic application program to find maximum number among two numbers.

Code:-

Private Sub Command1_Click ()

Dim a As Integer

Dim b As Integer

a = Val(Text1.Text)

b = Val(Text2.Text)

If (a > b) Then

        Label3.Caption = "a is maximum number"

Else

        Label3.Caption = "b is maximum number"

End If

End Sub


/*************************Output**************************/

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Program 5:-To create Visual Basic application program to perform arithmetic operations with the use of Option button.

Code:

Private Sub Option1_Click ()

Text3.Text = Val (Text1.Text) + Val (Text2.Text)

End Sub

Private Sub Option2_Click ()

Text3.Text = Val (Text1.Text) - Val (Text2.Text)

End Sub

Private Sub Option3_Click ()

Text3.Text = Val (Text1.Text) * Val (Text2.Text)

End Sub

Private Sub Option4_Click ()

Text3.Text = Val (Text1.Text) / Val (Text2.Text)

End Sub


/*************************Output**************************/

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