Netopedia: (34) Example OF NUMBER SYSTEM

Ques- conversion of decimal to binary number(42)_{10 =}(101010)
Ans – a r
42/2 = 21 0

21/2 = 10 1

10/2 = 5 0

2/2 = 1 0

1/2 = 0 1

Quest –convert to decimal no to binary number 73 to binary.
Ans- a r
73/2= 36 1

36/2= 18 0

18/2= 9 0

9/2= 4 1

4/2= 2 0

2/2= 1 0

Ans (73)₁₀=(1001001)₂

Que convertion of Decimal fraction to binary fraction.
Ans –
(81.635)₁₀ =(1010001.1010001)₂

A r

81/2 = 40 1

40/2 = 20 0

20/2 = 10 0

10/2 = 05 0

05/2 = 02 1

02/2 = 01 0

01/2 = 00 1

(81)₁₀=(1010001)₂

0.635*2 = 1.270 1

0.270*2 = 0.54 0

0.54*2 = 1.08 1

0.08*2 = 0.16 1

0.16*2 = 0.32 0

0.32*2 = 0.64 0

2. (0.81250₁₀ = (0. 1101)₂

0.8125*2 = 1.6250 1

1.6250*2 = 1.250 1

1.250*2 = 0.50 0

0.5*2 = 1.00 1

NOTE- the process will be continue for the seven (7) step.

Que. Conversion of decimal to octal number.
(63)₁₀= (77)₈

63/8 = 7 7

7/8 = 0 7

(256)₁₀= (400)₈

256/8 = 32 0

32/8 = 4 0

4/8 = 0 4

(1024)₁₀ = (2000)₈

1024/8 = 128 0

128/8 = 16 0

16/8 = 2 0

2/8 = 0 2

Que. Convertion of decimal fraction to octal fraction

(0.96)₁₀= (75341)₈

0.96*8 = 7.68 7

0.68*8 = 5.44 5

0.44*8 = 3.52 3

0.52*8 = 4.12 4

0.12*8 = 0.96 1

(110.01)₁₀ =( )₈

110/8 = 13 6

13/8 = 1 5

1/8 = 0 1

(110)₁₀=(156)₈

0.01*8 = 0.08 0

0.08*8 = 0.64 0

0.64*8 = 5.12 5

0.12*8 = 0.96 0

0.96*8 = 7.68 7

(0.1)₁₀= (0.0050)₈

(110.01) = (156.0057)₈

Note :- the process will continue to 5 step

Que:- convertion of decimal number to hexadecimal number

(426)₁₀= (1AA)₁₆

426/16 = 26 10

26/16 = 1 10

1/16 = 0 1

(1076)₁₀= (2409)₁₆

1076/16 = 672

672/16 = 42

42/16 = 2

2/16 = 0

Que:- convertion of decimal fraction to hexadecimal fraction

1. (0.25)₁₀ = (0.04)₁₆

0.25*16 = 4.00 = 4

2. (0.625)₁₀ = (0.10000A)₁₆

0.625*16 = 10.000

Que:-convertion of octal number to decimal number

1.(567)₈= (382)₁₀

5*8²+7*8¹+ 6*8⁰

5*64+56 +6

320+62 = (382)₁₀

2. (77)₈ = (63)₁₀

(77)₈= 7*8¹+ 7*8⁰

56+7

= (63)₁₀

_·Conversion of octol fraction to decimal fraction to decimal fraction.

_· (0.64)₈ = (0.8125)

_· (0.64)₈₌

0*8¹+6*8^-1+4*8^-2

0+6*1/8+4*1/8

3/4 +1/16

12+1/16

13/16

(0.8125)₁₀

2. (56.32)₁₀ = (46.40625)₁₀

(56.32)= 5*8¹+6*8⁰+3*8^-1+2*8^-2

40+6+3*1/8+2*1/64

46+3/8+1/32

(46.40625)¹⁰

Ques – conversion of binary number to decimal number .
(101010)₂= (42)¹⁰
(101010)₂₌ 1*2⁵+0*2⁴+1*2³+0*2²+1*2¹+0*2⁰

32+0+8+0+2+0

= (42)₁₀

2. (1001001)₂ =(73)₁₀

(1001001)₂= 1*2⁶+0*2⁵+0*2⁴+1*2³+0*2²+0*2¹+1*2⁰

= 64+0+0+8+0+0+1

= (73)₁₀

· Conversion of binary fraction to decimal fraction.

· (101001.101001)₂ =(41.640625)₁₀

(1001001)₂₌ 1*2⁶+0*2⁵+0*2⁴+1*2³+0*2²+0*2¹+1*2⁰

= 64+ 0+ 0+8+0+0+1

= (73)₁₀

Ques - conversion of binary fraction to decimal fraction.
1. (101001.101001)₂= (41.640625)₁₀
(101001.101001)₂= 1*2⁵+0*2⁴+1*2³+0*2²+0*2¹+1*2^-1+0*2^-2+1*2^-3+0*2^-4+0*2^-5+1*2^-6

= 32+0+8+0+0+1+1/2+0+1/8+0+0+1/64

= 41+1/2+1/8+1/64

= 2624+32+8+1/64

= (41.640625)₁₀

Ques – conversion of hexa decimal to decimal number.
1. (D3C)₁₆= d*16²+3*16¹+c*16⁰

13 *256++3*16+12*1

=(33.88)₁₀

^·2. (1AA)₁₆ =(426)₁₀

^·(1AA)₁₆= 1*16²A*16¹+A*16⁰

^·256+10*16+10*1

^·256+160+10

^·(426)₁₀

^·Ques – conversion of hexa decimal fraction to decimal fraction.

^· (D3C,A2)₁₆ = ( )₁₀

D*16²+3*16¹C*16⁰+A*16^-1+2*16^-2

13*256+3*16+12*1+10*1/16+1/16*16

= 3388+10/16+1/8*16

=3388+5/8+1/128

=433664+80+19/128

= 433745/128

= (3388.6328)₁₀

2. (D3E.D)₁₆ = (3390.8125)₁₀

= (D3E.D)₁₆= D*16²+3*16¹+E*16⁰+D*16^-1

= 13*256+48+14*1+13*1/16

= 3328+48+14+13/16

= 54240+13/16

= 54253/16

=(3390.8125)₁₀

NOTE- decimal
1. Binary (2).
2. Octal (8).
3. hexa decimal(16).
Ques – conversion of binary number to octol number.
(1110)₂=(16)₈

001110 ans .

2. (111111001)₂=(771)₈

· Conversion of binary fraction to octal fraction.

· (111111.110101110100)₂ = (771.6564)₈

2. (1110.01101)₂= (16.32)₈ ans .

RULE-the base of octal no is 8 but 8 is equal (=) to 2³ three for to convert a binary number to octal nimber make three type binary group of the binary number .

Ex - right to left .

Left to right.

3. (101101101101.110101101101)₂= (5555.6555)₈ans

· Conversion of octol number fraction to binary fraction

· (367421.11053)₈=(01111011110001000.001001000101010011)₂

· Conversion of binary number to Hexa decimal number.

· (101101)₂=(2d)₁₆

(00101101)=(213)₁₆=(2d)₁₆ans

2. (1100100101)₂= (325)₁₆

001100100101 =(325)₁₆

convertion of binary fraction to hexa decimal fraction.
(101101.11111)_{2 =} (2d.f8)₁₆

00101101.11111 =(2d.f8)₁₆

2.(1011110101.1100100101001)₂

00101111.1100100100101001= (215.1294)₁₆

₌ (2f5.c94)₁₆

RULE- the base of the fraction hexa decimal number 16 bit 2⁴ therefor to convert a binary number to hexa decimal make for byte binary group of the binary number.
Conversion of Hexadecimal fraction to Binary fraction-

1. (D3FA48.18CD86)₁₆= (110100111111101001001000.0011011110011000110)₂

2. (ACD.B4)₁₆=(101011001101.101101)₂

A C D B 4

1010 1101 1101 1011 0100

· Conversion of Octal number to Hexadecimal number-

1. Octal number

2. Binary number

3. Hexadecimal number

1. (235)₈=(9D)₁₆

(235)₈=(010011101)₂

2. (462)₈=(132)₁₆

(462)₈=(100110010)₂

(000100110010)=(132)₁₆

Conversion of Octal fraction to Hexadecimal decimal-

(462.571)₈=(132.BC8)₁₆

(462.571)₈=(100110010.101111001)₂

(000100110010.1011110010000)₂

=(132.1128)₁₆=(132.BC8)₁₆

· Conversion of Hexadecimal number to octal number-

RULE- Hexadecimal number

Binary number

Octal number

1. (AD4)₁₆=(5324)₈

(AD4)₁₆=(101011010100)₂

(101011010100)₂=(5324)₈

· Conversion of Hexadecimal fraction to Octal fraction-

(AD4.35)₁₆= (5324.152)₈

(AD4.35)₁₆=(101011010100.00110101)₂

=(10101101000.00110101010)

(5324.152)₈

Netopedia

Monday, July 22, 2019

(34) Example OF NUMBER SYSTEM

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