Patent Application: US-84949104-A

Abstract:
a dna based number system and basic arithmetic operations i . e . addition and subtraction for this have been developed . the method of invention comprises assignment of arbitrary integer values to all dna bases , arbitrary assignment of complements of dna bases , representation of integers and real numbers in terms of dna bases and performing basic arithmetic assignment on dna based number system . this will find wide application in the area of dna or other molecular computation devices and processors .

Description:
the present invention relates to a dna based number system and arithmetic . more particularly , the present invention relates to a dna based number system and arithmetic which comprises assignment of arbitrary values to all dna bases , arbitrary assignment of complements of dna bases , representation of integers and real numbers in terms of dna bases and performing basic arithmetic assignment on dna based number system . in the system of the invention there are 4 elements in dna based number system . these elements are “ a ”, “ t ”, “ c ”, “ g ”. arbitrary values assigned to each element of the dna based number system are : a = 0 , t = 1 , c = 2 , g = 3 . integers can be represented in the form of 8 bases / cell . the value of base in the dna based number system is positional . complement representation is used to represent integers . however , positive integers don &# 39 ; t have complements . the assigned complements to the elements of dna based number system are : complement of a = g , complement of t = c and vice - versa . conversion of positive integers to dna based number is done by dividing the number by 4 and extracting the remainder , continuing this procedure until the quotient becomes zero . the first remainder digit extracted as the least significant base ( lsb ), the last extracted digit will be marked as main significant base ( msb ). the dna based number is obtained by writing the bases extracted left to right from msd to lsd . the cell is then completed ( 8 - bases / cell or its multiple ) by adding extra padding to the left as a &# 39 ; s and putting leftmost base as sign base i . e . “ a ” for positive integer . leftmost base would represent the sign of the number . the conversion of negative numbers to dna based numbers is done by first taking the number as positive integer , converting it to dna based number system as discussed above , producing its complement by changing as to gs , ts to cs and vice versa , adding a base t (= 1 ) to the complement , completing the cell ( 8 - bases / cell or its multiple ) by adding extra padding to the left as g &# 39 ; s and putting leftmost base as sign base i . e . “ g ” for negative integer . leftmost base would represent the sign of the number . positive real numbers are converted to dna based number by first converting the real number to an integer by shifting the decimal point to the right . this integer is then converted to dna based number as discussed above with respect to positive integers . the number of points shifted is recorded and represented as an exponent ( utilizing integer to dna based conversion scheme mentioned above ). the leftmost base represents sign base of the number , next 23 - bases represent the magnitude and the rest 8 - bases represent the exponent . in the method of the invention , the sign base in the case of positive real number is be “ t ” and sign base in the case of negative real number is “ c ”. for the conversion of negative real numbers to dna based number the real number is first taken as positive real number and this real number then converted to an integer by shifting the decimal point to the right . this integer is then converted to dna based number as in the case of positive integer to dna based number conversion discussed above . the complement of resulting dna based number is produced by changing a &# 39 ; s to g &# 39 ; s , t &# 39 ; s to c &# 39 ; s and vice versa and a base t (= 1 ) is then added to the complement . the number of decimal points shifted is recorded and represented as exponent ( utilizing integer to dna based conversion scheme mentioned above ). the leftmost base represents sign base of the number , next 23 - bases represent the magnitude and the rest 8 - bases represent the exponent . the number system of the invention is useful in the creation of quad - state computing devices since the system has four elements and is not limited to the two elements of the binary system . this therefore enables representation of larger numbers when compared to the conventional binary system and therefore enables design and fabrication of powerful dna based computing devices . the invention will now be described with reference to the accompanying examples which are illustrative and should not be construed as limiting the scope of the invention in any manner . s . no . description dna based number 1 . decimal number to integers are represented as 8 bases / cell dna based number leftmost base represents the sign of the integer conversion decimal number to dna based number conversion 4 100 remainder 4 25 0 = a lsd 4 6 1 = t 4 1 2 = c 0 1 = t msd 2 . limits to integer maximum : + 4 n − 1 − 1 representation in n minimum : − 4 n − 1 bases / cell 3 . integer addition addition of 100 and 63 : 4 . integer subtraction subtracting 63 from 100 : sol . complement of ( 63 ) 10 is taken and added to ( 100 ) 10 note : extra carry t has to be ignored 5 . real number real numbers are represented as floating - point in 32 - bases / cell . representation having three components i . e . sign bit , magnitude and exponent : − leftmost base represents the sign + next 23 bases represent the magnitude + rest 8 bases represent exponent − sign base “ t ” represents positive real number − sign base “ c ” represents negative real number 6 . real number addition of 1 . 1 and 1 . 1 addition soln . magnitude is taken for prcocessing : 7 . real number subtracting 12 . 3 from 10 . 1 subtraction soln . addition of 10 . 1 and − 12 . 3 would give the result 1 . braun , e ., eichen , y ., sivan , u . & amp ; 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