This presentation is all about the computer number system.

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School of Computer Science & Application
Subject:- Computer Fundamentals Organization
Name: Raj Agrawal
Roll no.: 01
Branch: BCA CTIS (sem: 1)
Guided By: Prof. Swapnil Dixit Sir

2. What is Number System
The number system that we use in our day-to-day life is the decimal number system. Decimal
number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the
successive positions to the left of the decimal point represent units, tens, hundreds, thousands
and so on.
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3. Conversion Among Bases
DECIMAL
HEXADECIMALBINARY
OCTAL
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4. Binary To Decimal
 Technique
• Multiply each bit by 2n , where n is the “weight” of the bit
• The weight is the position of the bit, starting from 0 on the right
• Add the results
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Multiplication Result
1 x 20 1
1 x 21 2
0 x 22 0
1 x 23 8
0 x 24 0
1 x 25 32
Answer 4310
Convert the number 110101 from Binary to Decimal

5. Octal To Decimal
 Technique
• Multiply each bit by 8n, where n is the “weight” of the bit
• The weight is the position of the bit, starting from 0 on the right
• Add the results
Multiplication Result
4 x 80 4
2 x 81 16
7 x 82 448
Answer 46810
Convert the number 427 from Octal to Decimal
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6. Hexadecimal To Decimal
 Technique
• Multiply each bit by 16n, where n is the “weight” of the bit
• The weight is the position of the bit, starting from 0 on the right
• Add the results
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Multiplication Result
9 x 160 9
8 x 161 128
5 x 162 1280
Answer 1417
Convert the number 985 from Hexadecimal to Decimal

7. Hexadecimal to Binary
 Technique
• Convert each hexadecimal digit to a 4-bit equivalent binary representation
Convert the number 10AF16 from Hexadecimal to Binary
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
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8. Decimal to Binary
 Technique
• Divide by two, keep track of the remainder.
• First remainder is bit 0 (LSB, least-significant bit).
• Second remainder is bit 1, etc.
Convert 1310 from Decimal to binary
Division By 2 Quotient Remainder Bit#
13/2 6 1 0
6/2 3 0 1
3/2 1 1 2
½ 0 1 3
Answer 11012
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9. Octal To Binary
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Technique
• Convert each octal digit to a 3-bit equivalent binary representation
7 0 5
111 000 101
Convert the number 7058 from Octal to Binary
7058 = 1110001012

10. Octal to Hexadecimal
Technique
• Convert to binary: 011 110 100 010 101 001 000 011
• Regroup in 4s (from the end): 0111 1010 0010 1010 0100 0011
• Recode as Hex
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11. Binary to Decimal
Multiplication Result
1 x 2-4 0.0625
1 x 2-3 0.125
0 x 2-2 0.0
1 x 2-1 0.5
0 x 2-0 0.0
1 x 21 2.0
Answer 2.6875
Convert the number 10.1011 from Binary to Decimal
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12. Thank You…!
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