Number System

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.

• 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

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)

• (1X2)4+(0X2)3+(1X2)2+(0X2)1+(1X2)0=16+0+4+0=1=21

• 10101=2110

• Binary digit is bit

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=1071

• 20578=107110

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

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

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

THANK YOU