文档介绍：Digital concept and Number system
Chapter 1
Number systems
Number system use positional notation to represent value. The position of the character (numeral) in a character string (collection of possible numerals) indicate value as well as the character itself.
Radix (base) is the number of numeral characters in the character set of a positional number system.
Position Weight is a constant that represents the value of a position. Different position has different weight. It is the integer power of radix.
Radix = r;
Weight = rn;
Character set = { 0, 1, ………, r-1 }
Represent number N of radix r
Positional Notation
(N)r = Cn-1Cn-2…Ci…C0•C-1C-2….C-m
Polynomial Notation
(N)r = Cn-1rn--2rn-2+…+Ciri+…+C0r0
+C-1r-1+C-2r-2+….+C-mr-m
n is the number of digits in the integer portion of N, m is the number of digits in the fractional portion of N
Counting in Base r
Decimal number
Radix=10 ;
Character set : {0,1,2,3,4,5,6,7,8,9}
Weight=10n ;
Ex. The decimal number 536 is (536)10
Binary number
Radix=2 ;
Character set :{0,1}
Weight=2n ;
Ex. The binary number 0110 is (0110)2
Octal number
Radix=8 ;
Character set : {0,1,2,3,4,5,6,7}
Weight=8n ;
Ex. The decimal number 536 is (536)8
Hexadecimal number
Radix=16 ;
Character set : {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
Weight=16n ;
Ex. ()16=1 * 162+A * 161+D * 160+B * 16-1
Binary To Hexadecimal Conversion
Solution:
1. Partition the binary number into groups of four, starting at the radix point and going left and right.
2. Each group of four corresponds to a single hexadecimal digit.
Binary To Octal Conversion
Solution:
1. Partition the binary number into groups of three, starting at the radix point and going left and right.
2. Each group of three corresponds to a single octal digit.
Octal ,Hexadecimal to Binary conversion
Solution:
Each hexadecimal digit corresponds to four binary digits.
Each octal digit corresponds to three binary digits
Binary To Decimal Conversion
Solution:
Polynomial Notation
(N)2 = Bn-1*2n-1+Bn-2 * 2n-2+…