Lec 2. (Computer Science) Bit, Byte Bit means 0 or 1 i.e. on or off, it's ...

<strong>Lec</strong> <strong>2.</strong>(<strong>Computer</strong> <strong>Science</strong>)<strong>Bit</strong>, <strong>Byte</strong><strong>Bit</strong> <strong>means</strong> 0 <strong>or</strong> 1 i.e. on <strong>or</strong> off, it’s the basic unit in processing the data becauseall the data are converted to bits in digital computers.<strong>Byte</strong> is the mem<strong>or</strong>y size in which one symbol <strong>or</strong> number from 0 to 255 isst<strong>or</strong>ed, it consists of 8 bits.Kilobyte (KB) equals 1024 byte (2 10 ) f<strong>or</strong> example a mem<strong>or</strong>y with 64KBdoesn’t mean 64000byte it <strong>means</strong> 1024*64= 65536byte.Mega <strong>Byte</strong> (MB) equal 2 20 byte, Giga <strong>Byte</strong> (GB) equal 2 30 byte and Tera<strong>Byte</strong> (TB) equal 2 40 byte (kilo <strong>means</strong> thousand, mega <strong>means</strong> million, giga<strong>means</strong> billion and tera <strong>means</strong> trillion).Numbering systemThere are four numbering systems1. decimal (base=10)<strong>2.</strong> binary (base=2)3. octal (base=8)4. hexadecimal (base=16)Basics of numbering system1. Each numbering systems is named acc<strong>or</strong>ding to its base number (base= B)which is used in its calculations.<strong>2.</strong> The numbers of symbols in each system are {0, 1, 2, ……, B-1}.3. F<strong>or</strong> system with n ranks the biggest number is B n -1.4.Symbol in the further most right rank in any system is called Leastsignificant Digit-LSD, symbol in the further most left rank is called MostSignificant Digit-MSD.5. F<strong>or</strong> system with base B ,n= number of ranks f<strong>or</strong> integerAnd m= number of ranks f<strong>or</strong> fraction part thenDecimal value = a n-1 a n-2 …… a 1 a 0 . a --1 a --2 …. a -mThis value is calculated usinga n-1 b n-1 +a n-2 b n-2 ... +a 1 b 1 + a 0 b 0 + a -1 b -1 + a -2 b -2 +…+ a -m b -m Eqn. (1)6.All systems use one method to convert to decimal and vice versa the onlydeference is in base value.Decimal system:it is the same as the one we use in our lives, Eachdecimal rank weight 10 times its right neighb<strong>or</strong> in this way the weights ofthe ranks from left to right is 1,10, 100, 1000 and so on.1

Base =10 The symbols used are{0,1, 2,3,4,5,6,7,8,9}E.x. value of 29029.98 is:2*10 4 +9*10 3 +0*10 2 +2*10 1 +9*10 0 +9*10 -1 +8*10 -2 Binary system<strong>Computer</strong> uses binary system its base is 2 and it contain only 0 <strong>or</strong> 1(on <strong>or</strong> off)In binary system each rank weight twice its right neighb<strong>or</strong> in this way rankweights from left to right is 1, 2, 4, 8, 16 and so on. Base =2 The symbols used are {0,1}Converting from any system to decimal:-We can use equation (1) to convert the number in any system to decimale.x. Convert (110101.1101) 2 to decimalSol.Using equation 1a n-1 b n-1 +a n-2 b n-2 ... +a 1 b 1 + a 0 b 0 + a -1 b -1 + a -2 b -2 +…+ a -m b -m Eqn. (1)110101.1101 = a 5 a 4 a 3 a 2 a 1 a 0 . a -1 a -2 a -3 a -4 , n=6 , m=4a 5 b 5 +a 4 b 4 + a 3 b 3 +a 2 b 2 +a 1 b 1 + a 0 b 0 + a -1 b -1 + a -2 b -2 + a -3 b -3 +a -4 b -4f<strong>or</strong> binary system base =2 then b=21*2 5 +1*2 4 + 0*2 3 +1*2 2 +0*2 1 + 1* 2 0 + 1*2 -1 + 1* 2 -2 + 0*2 -3 +1*2 -4=32+16+0+4+0+1+0.5+0.25+0+0.0625=53.8125E.x. convert (11001.101) 2 to decimalSolution:1*2 4 +1*2 3 +0*2 2 +0*2 1 +1*2 0 +1*2 -1 +0*2 -2 +1*2 -3 =16+8+0+0+1+1/2+0+1/8=(25.625) 10e.x.The value of (10101.01) 2 in decimal system is1*2 4 +0*2 3 +1*2 2 +0*2 1 +1*2 0 +0*2 -1 +1*2 -2 =21.252