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02-Jun-2015View

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Number System, BIT, Byte

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- 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 =0,1 110012 10. THANK YOU

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