Digital concept an Number system Chapter 1 Number systems
Digital concept and Number system Chapter 1 Number systems
Positional Nmber Sestem 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
• 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
Countingin Base rar Systen Radix=r Weight Character set =[0, 1,. ,r-13 Represent number n of radix r Positional notation (N)=Cn1Cn2.C…,Co°C1C2 Polynomial Notation (N=Cn-rh-1+Cn-2rn-2++C;ri++Coro +Cr1+C2r2+…+Cnr n is the number of digits in the integer portion of n, m is the number of digits in the fractional portion of n
• 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-1r n-1+Cn-2r n-2+…+Cir i+…+C0r 0 +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
Positional Nmber Selen e Decimal number Radix=10 Character set:{0,1,2,34,5,6,7,8,9} 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
• 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
Positional Nmber Selen ° Octal number Radix=8 Character set: 10, 1, 2, 3, 4, 5, 6, 7 Weight=8n Ex. The decimal number 536 is(536) ● 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.(1AD.B)6=1*162+A*161+D*160B*16-1
• 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. (1AD.B)16=1 * 162+A * 161+D * 160+B * 16-1
Positional Nmber Sestem 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 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
Positional Nmber Sestem 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 dig计t
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
Positional Nmber Sestem Octal, Hexadecimal to Binary Converson Solution: Each hexadecimal digit corresponds to four binary digits Each octal digit corresponds to three binary digits
Octal ,Hexadecimal to Binary conversion • Solution: – Each hexadecimal digit corresponds to four binary digits. – Each octal digit corresponds to three binary digits
Positional Nmber Sestem Binary To Decimal Conversion Solution Polynomial Notation (N)2=Bn12m+Bn2*2m2++B1*2++Bo*20 B1*2-1+B 2 B*2 Evaluate each term in the Polynominal
Binary To Decimal Conversion • Solution: – Polynomial Notation (N)2 = Bn-1 *2n-1+Bn-2 * 2n-2+…+Bi * 2i+…+B0 * 20 +B-1 * 2-1+B-2 * 2-2+….+B-m * 2-m – Evaluate each term in the Polynominal
Positional Nmber Sestem Any Radix To Decimal Conversion Solution Polynomial Notation (N)n=Cn1*rn1+Cn2*rn2+…+C1r+…+C0*r0 C.1*r-1+C2* 2+,…t+( Evaluate each term in the Polynomial
Any Radix To Decimal Conversion • Solution: – Polynomial Notation (N)r = Cn-1 *r n-1+Cn-2 * r n-2+…+Ci * r i+…+C0 * r 0 +C-1 * r -1+C-2 * r -2+….+C-m * r -m – Evaluate each term in the Polynomial
