sneha. number system number system types of number system types of number system types of...
TRANSCRIPT
![Page 1: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/1.jpg)
sneha
![Page 2: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/2.jpg)
Number System Types of Number System Types of positional number system Binary to Decimal Octal to Decimal Hexadecimal to Decimal Decimal to Binary Octal to Binary Hexadecimal to Binary Decimal to Octal
![Page 3: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/3.jpg)
Decimal to Hexadecimal Binary to Octal Binary to Hexadecimal Octal to Hexadecimal Hexadecimal to Octal Exercise – Convert ...
![Page 4: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/4.jpg)
A A number systemnumber system defines how a number can be represented defines how a number can be represented using distinct symbols. A number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two differently in different systems. For example, the two numbers (2A)numbers (2A)1616 and (52) and (52)88 both refer to the same quantity, both refer to the same quantity, (42)(42)1010, but their representations are different. , but their representations are different.
Several number systems have been used in the past and can Several number systems have been used in the past and can be categorized into two groups: be categorized into two groups: positionalpositional and and non-positionalnon-positional systems. Our main goal is to discuss the positional number systems. Our main goal is to discuss the positional number systems, but we also give examples of non-positional systems, but we also give examples of non-positional systems.systems.
![Page 5: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/5.jpg)
Two types of Number System
1) Positional No System
2) Non- Positional No System
![Page 6: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/6.jpg)
Various positional number system:
1) Binary number system
2) Decimal number system
3) Octal number system
4) Hexadecimal number system
![Page 7: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/7.jpg)
The possibilities
Hexadecimal
Decimal Octal
Binary
![Page 8: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/8.jpg)
2510 = 110012 = 318 = 1916
Base
![Page 9: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/9.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 10: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/10.jpg)
Technique1) Multiply each bit by 2n, where n is the “weight” of the
bit2) The weight is the position of the bit, starting from 0 on
the right3) Add the results
![Page 11: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/11.jpg)
1010112 => 1 x 20 = 11 x 21 = 20 x 22 = 01 x 23 = 80 x 24 = 01 x 25 = 32
4310
Bit “0”
![Page 12: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/12.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 13: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/13.jpg)
Technique1) Multiply each bit by 8n, where n is the “weight” of the
bit2) The weight is the position of the bit, starting from 0 on
the right3) Add the results
![Page 14: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/14.jpg)
7248 => 4 x 80 = 42 x 81 = 167 x 82 = 448
46810
![Page 15: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/15.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 16: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/16.jpg)
Technique1) Multiply each bit by 16n, where n is the “weight” of the
bit2) The weight is the position of the bit, starting from 0 on
the right3) Add the results
![Page 17: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/17.jpg)
ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560
274810
![Page 18: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/18.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 19: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/19.jpg)
Technique1) Divide by two, keep track of the remainder.2) If remainder is zero then it track zero3) If remainder is not zero then it track 1
![Page 20: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/20.jpg)
12510 = ?22 125 62 12 31 02 15 12 7 12 3 12 1 12 0 1
12510 = 11111012
![Page 21: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/21.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 22: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/22.jpg)
Technique◦ Convert each octal digit to a 3-bit equivalent
binary representation
![Page 23: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/23.jpg)
7058 = ?2 7 0 5
111 000 101
7058 = 1110001012
![Page 24: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/24.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 25: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/25.jpg)
Technique◦ Convert each hexadecimal digit to a 4-bit equivalent
binary representation
![Page 26: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/26.jpg)
10AF16 = ?2 1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
![Page 27: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/27.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 28: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/28.jpg)
Technique1) Divide by 82) Keep track of the remainder
![Page 29: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/29.jpg)
123410 = ?8
8 1234 154 28 19 28 2 38 0 2
123410 = 23228
![Page 30: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/30.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 31: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/31.jpg)
Technique1) Divide by 162) Keep track of the remainder
![Page 32: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/32.jpg)
123410 = ?16
123410 = 4D216
16 1234 77 216 4 13 = D16 0 4
![Page 33: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/33.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 34: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/34.jpg)
Technique1) Group bits in threes, starting on right2) Convert to octal digits
![Page 35: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/35.jpg)
10110101112 = ?8
1 011 010 111
1 3 2 7
10110101112 = 13278
![Page 36: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/36.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 37: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/37.jpg)
Technique
1) Group bits in fours, starting on right2) Convert to hexadecimal digits
![Page 38: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/38.jpg)
10101110112 = ?16
10 1011 1011
2 B B
10101110112 = 2BB16
![Page 39: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/39.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 40: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/40.jpg)
Technique◦ Use binary as an intermediary
![Page 41: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/41.jpg)
10768 = ?16
1 0 7 6
001 000 111 110
2 3 E
10768 = 23E16
![Page 42: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/42.jpg)
Hexadecimal
Decimal Octal
Binary
![Page 43: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/43.jpg)
Technique◦ Use binary as an intermediary
![Page 44: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/44.jpg)
1F0C16 = ?8
1 F 0 C
0001 1111 0000 1100
1 7 4 1 4
1F0C16 = 174148
![Page 45: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/45.jpg)
Decimal Binary Octal
Hexa-decimal
33
1110101
703
1AF
![Page 46: Sneha. Number System Number System Types of Number System Types of Number System Types of positional number system Types of positional number system](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649f315503460f94c4cd17/html5/thumbnails/46.jpg)
Decimal Binary Octal
Hexa-decimal
33 100001 41 21
117 1110101 165 75
451 111000011 703 1C3
431 110101111 657 1AF
Answer