The document discusses different number systems including decimal, binary, octal, and hexadecimal. It explains that in a positional number system, the value of each digit depends on its position, with the rightmost being the ones place and each place to the left representing higher powers of the base. For decimal, the base is 10 with digits 0-9. Binary uses only 0s and 1s with a base of 2. Octal uses digits 0-7 with a base of 8. Hexadecimal uses digits 0-9 and A-F, with a base of 16. Converting between number systems involves determining the place value of each digit and summing the products of each digit and its place value.

1. Number
System

2. Intro
• All the computers store numbers ,letters and
other special characters in a coded form. So
its very important to understand number
system to have better understanding .
• Number System:
• Non-Positional- counting on fingers, we have
symbols,1,2,3 etc. each represents Fist value
regardless of its position in a number
• Positional- Few symbols called digits. They
represent diff values depending on the position
they occupy.

3. • The digit itself
• The position of the digit in the number
• The base( base is total number in digits)
• DECIMAL NUMBER SYSTEM
• base is 10 (0,1,2,3,4,5,6,7,8,9)
• ones
,tens,hundreds,thousands,tenths,100ths.million
• 2586 – 258610
• 2X1000+5X100+8X10+6X1=2000+500+80+6
• Same digits diff values if relocated.
• 6852

4. Binary Number System
• Like Decimal system but base is 2 instead of
10
• Only two symbols 0,1
• Largest number 1 (on less than base)
• Each position in binary system represents a
power of base (2)
• The right most position in units (2)0,(2)1
• Decimal equivalent of binary num 10101
(101012)

5. • (1X2)4+(0X2)3+(1X2)2+(0X2)1+(1X2)0=16+0+4+
0=1=21
• 10101=2110
• Binary digit is bit

6. Octal Number System
• Base is 8 (0,1,2,3,4,5,6,7) no 8,9
• Each position represents power of base
• 2057
• (2x8)3+(0x8)2+(5x8)1+(7x8)=1024+0+40+7=1
071
• 20578=107110

7. Hexadecimal Number System
• Base is 16
• 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
• 10,11,12,13,14,15
• Largest digit 15 one less than base (16)
• Position represents power of base
• 1AF
• (1x16)2+(Ax16)1+(Fx16)0=256+160+15=431
• 1AF16=43110

8. Converting another Base to
Decimal
• Determine the column positional value of
each digit
• Multiply the obtained column value by digit
in the column values bys the digits in the
corresponding column
• Sum up the products calculated
• 11001=(2)4+(2)3+(2)2+(2)1+2=2510

9. Decimal to Another Base
• Divide decimal number by the value of new base
• Record the remainder from step 1 as the rightmost of the
new base number
• Divide the quotient of the previous division by new base
• Record the remainder from 3 step as next digit of new
base num
• 2510=25/2 12-1
• 12/2= 6,0
• 6/2=3,0
• 3/2=1,1
• ½=0,1
• 110012

10. THANK YOU