Number system

1. Number system • Numbers • 1) natural number: zero and any number obtained by repeatedly adding one to it i.e 100,653 2) negative number: a value less then 1, with a – sign i.e -24,-1 3) integer: a natural number, a negative number, zero i.e 248,0,-23

2. Number system • A set of values used to represent different quantities is called number system • i.e 1) number of student in class 2) number viewers watching TV. There are four number system are as fellow: • Binary number system • Decimal number system • Octal number system • Hexadecimal number system

3. Decimal number system • The decimal number consist of 10 digits from 0 to 9. • These digits can be used to represent d/f any numeric value. • The base of decimal nuber system is 10. • It is most widely used number system. • The value represented by each digit depend on position and weight of digit. • The value of number is determined by multiplying the digits with the weight of their position and adding the result. This method is called expension method.

4. The right most digit of a number has the lowest weight. This digit is called least significant digit. • The left most digit of a number has the highest weight. This digit is called most significant digit. • The decimal number system is also called base ten or occasionally denary. • Example: 453 • Position: 2 1 0 • Weight: 102 101 100 • Face value: 4 5 3 • 453 = 4*102+5*101+3*100 453 = 400+50+3 the actual number can be found by adding the values obtained by the digit.

5. Binary number system Binary : it consist of 2 digits 0 and 1called bit. Byte: collection of 8 bits called 1 byte. Word: word consist of group of bits which are pressed around together during computition. * The word length of the computer system or processor is how many bits are grouped together.

6. 8 bit machine (i.e Nintendo Gameboy) • 16 bit machine(sega genesis) • 32 bit machine(sonyplaystation) Binary number system 1) Digital computer are made up of electronic circui, which have exactly 2 ststes:ON and OFF. 2) Computer used numbering system which has exactly 2 symbols, representating on and off. 3) The base of binary number system is 2. 4) Each digit or bit in binary number system is 0 or 1. 5) Binary number system are built by concatenating a string of bits together.

7. As a general form: dn*bn-1 + dn-1*bn-2+……………….+d1*b0 n: number of digits in number. b: base d: digit i.E: 1011 When written,binary number are often subscripted,prefixed or suffixed in order to indicate their base. The following notations are equivalent: 1011binary (explicit statement of fomat) 10111b (a suffix indicating binary format) 01101B (a suffix indicating binary format) 011012 (a subscript indicating base-2(binary))

8. Base / Radix: • The total number of digits used in number system is called its base or radix.

9. Binary Numbers • Internally, information in digital systems is of binary form • groups of bits (i.e. binary numbers) • all the processing (arithmetic, logical, etc) are performed on binary numbers. • Example: • In decimal, (100101)2 • Convention: write only the coefficients. • A = a1 a0 . a-1 a-2 a-3 whereaj  {0, 1, …, 9} • How do you calculate the value of A?

10. Decimal system • coefficients are from {0,1, …, 9} • and coefficients are multiplied by powers of 10 • base-10 or radix-10 number system • Using the analogy, binary system {0,1} • base(radix)-2 • Example: 25.625 • 25.625 = decimal expansion • 25.625 = binary expansion • 25.625 = • base-r (n, m) • A = an-1 rn-1 +… +a1 r1 +a0 r0 + a-1 r-1 + a-2 r-2 + … +a-m r-m