Number system Numbers 1 natural number zero and
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
Number system 1) A set of values used to represent different quantities is called number system 2) i. e 1) number of student in class 2) number viewers watching TV. There are four number system are as fellow: 1) Binary number system 2) Decimal number system 3) Octal number system 4) Hexadecimal number system
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.
• 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.
Binary number system Binary : it consist of 2 digits 0 and 1 called 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.
• 8 bit machine (i. e Nintendo Gameboy) • 16 bit machine(sega genesis) • 32 bit machine(sony playstation) 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.
• As a general form: dn*bn-1 + dn-1*bn-2+………………. +d 1*b 0 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: 1011 binary (explicit statement of fomat) 10111 b (a suffix indicating binary format) 01101 B (a suffix indicating binary format) 011012 (a subscript indicating base-2(binary))
• Base / Radix: • The total number of digits used in number system is called its base or radix.
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 = a 1 a 0. a-1 a-2 a-3 where aj {0, 1, …, 9} • How do you calculate the value of A?
• 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 +… + a 1 r 1 + a 0 r 0 + a-1 r-1 + a-2 r-2 + … +a-m r-m
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