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Is Hirihiti?H DECIMAL May 1, 1962 J. F. COULEUR 3,032,266 DECIMAL TO BINARY CONVERSION OF NUMBERS LESS THAN UNITY Filed July 12, l960 2 Sheets-Sheet l FG.I. TENTHS DECADE HUNDREDTHS DECADE THOUSANDTHS DECADE 4. 2 is hirihiti?h DECIMAL TERAF DODE MATRIX DODE MATRIX DODE MATRIX TEST PULSE BUS CLOCK - MULTIVBRATOR AND BNARY COUNTER ACCUMULATOR NVENTOR: JOHN F. COULEUR, BY (4-f (? W2----- HIS AT TORNEY. May 1, 1962 J. F. COULEUR 3,032,266 DECIMAL TO BINARY CONVERSION OF NUMBERS LESS THAN UNITY Filed July 12, 1960 2. Sheets-Sheet 2 F.G.3. BINARY BINARY CODED DECMAL TENTHS HUNDREDTHS THOUSANDTHS Row 3 2 8 NUMBER O O OOO OOO () OO OOO O T (2) O O O O O OO S (3) O OO OOO OO T (4) O OO OOO OOO S (5) O OO OOO OOO T (6) OO O O OOO OOO S (7) OO OO OOO OOO T (8) OO OOO OO O OOO S (9) OO OOO OOO O T (O) OOO OOO OO OO S (I) OOO OOO OO OO T (2) OOOO OO OO OOO S (3) OOOO OO OO OOO T (4) OOOO OO OOO OO O S (5) OOOO OO O OOO. T (6) OOOO OO OO OOO S (7) OOOO OO OO O T (8) OOOO OO OO O O S (9) OOOO OO OO OO T (20) OOOO OOO O OO O S (2) T MEANS TEST AND ADD THREE TO ANY DECADE 2 5 S MEANS SHIFT FIG.4. BINARY BNARY CODED DECMA -------------------IO- IO-2 IO-3 IO-4 10-5 O-6 (3) (2) (8) () (2) (5) OO OOO OOO OOO OOO OO OO OOO O OOO OOO OOO T O O O Oi Oi O O OOO O. O. O. S O OO OOO OO OOO OOO T Of OO OOO OOO Oi Oi O S O OO OOO OOO OOO T OO Oi O OOO O. O. O. S O. O. O. O. OOO OOO T O O OOO OO O S O O OOO OOO T O O O O. O. O S O O O (OOO T O. O. O. O. S SE SHIFT Te TEST AND ADD THREE TO ANY DECADE 25 INVENTOR JOHN F. COULEUR, HIS AT TORNEY. 3,032,266 United States Patent Office Patented May 1, 1962 2 the data mor tractable to machine techniques. For a 3,032,266 DECMAL TO BINARY CONVERSION OF NUM more complete discussion of arithmetic or number sys BERS LESS THAN UNITY tems reference is made to a book entitled "High Speed John F. Couleur, Fayetteville, N.Y., assignor to General Computing Devices” written by the Staff of Engineering Electric Company, a corporation of New York 5 Research Associates Incorporated and published by Mc Filed July 12, 1960, Ser. No. 42,337 Graw Hill, New York, 1950, or to a book entitled "Arith 7 Claims. (C. 235-155) metic Operations in Digital Computers" written by R. K. Richards and published by D. Van Nostrand Company, This invention relates to a method and apparatus for New York, 1955. converting a representation of data in a first number sys 10 It has long been known that the arithmetic process of tem to an equivalent representation in a second number converting a pure decimal fraction to a pure binary frac system. More particularly, this invention relates to a tion consists of repeated multiplication of the decimal method and apparatus for converting a binary coded deci number by 2. the binary number base, and noting the carry mal number having a value less than unity, i.e., a binary after each multiplication. See, for example, page 287 of 1 coded decimal fraction, to a pure binary number. the second above noted book. A similar arithmetic proc The converse problem of converting a pure binary ess is applicable to the conversion of binary coded decimal number having a value less than unity, i.e., a binary frac fractions to pure binary fractions. The instrumentation tion, to a binary ccded decimal number forms the Sub of this process, however, using standard multiplication ject matter of an application entitled, "Binary to Decimal techniques has in the past required cumbersome and ex Conversion of Numbers Less Than Unity,' filed by John 20 pensive equipment and has been excessively time consum F. Couleur concurrently herewith and assigned to the ing. The problems of entering fractional binary coded same assignee as the present application. Parallel prob decimal keyboard data to a pure binary computer system lems of converting whole numbers, or integers, from one or of utilizing fractional binary coded decimal output data radix to another have been treated in two co-pending ap from a decimal computer system in a pure binary com plications filed together by John F. Couleur on October 7, 25 puter system, for example, have in the past been solved by 1957, and assigned to the same assignee as is the instant using either a miniature computer or a time consuming invention. These two applications are, respectively, Serial counting process in order to perform the necessary con Number 688,509 entitled "Binary to Decimal Conver version from one number system to the other. sion' and Serial Number 688,589 entitled "Decimal to It is therefore an object of this invention to provide a Binary Conversion.” 30 method and apparatus for rapidly and economically con It is well known in the digital computing arts that any verting a representation of data in a first number system to given number can be expressed in many different number an equivalent representation of data in a second number systems each using a different number base or radix. The System. number system in common everyday use is, of course, the It is a more specific object of this invention to provide a decimal system in which a base or radix of ten is used. 35 method and apparatus for converting a binary coded de Each digit of a number is then understood to be a multi cimal number having a value less than unity to a pure plier or coefficient of a power of ten, the power implied binary number. increasing frcm right to left in accordance with the posi It is a still further object of this invention to provide a tional significance of the digit. Thus, the decimal number new and improved method and apparatus for processing 0.3281.25 may be explicitly written as 3x10-1-1-2X 10-2 40 data. --8x10-3-1-1 x 10-4-4-2x10-5--5X 10-6. Although many Briefly, in accordance with one aspect of this invention, digital computers have been built which are designed to a decimal fraction or a decimal number less than unity operate on an essentially decimal basis, many of the more having N digits is represented in binary coded decimal modern digital computers are designed to operate on data form and read into a shift register such as is shown on expressed in pure binary notation rather than in decimal pages 144-148 of the reference "Arithmetic Operations notation. In the binary system, of course, a number in Digital Computers' where the registers have 4N stages base of two is used in place of the number base or radix grouped to form N decades with the content of each de ten used in the decimal system. Thus, the decimal num cade representing one digit of said decimal number. The . ber 0.09 may be explicitly written in pure binary form as conversion process consists of shifting this binary coded 50 decimal fraction out of the register one digit at a time, 0x2-1--0x2-2-1-0x2-8--1x2-4 . most significant digit first, testing the magnitude of the --1X2-5-1x2-6-1x2-7-1-1 X2-8 content of each decade following each shift after the first More briefly, this binary nine-hundredths is commonly shift, adding binary three to any decade, the binary con written as 0.00011111 wherein the number base two is tent of which is equal to or greater than five when tested, implied and only the coefficients are expressed. Further 55 and terminating the steps with a last shift. The output. more, those computers which do operate on decimal data of the register can then be shown to be a pure binary frequently use a number system known as binary coded representation of the binary coded decimal fraction orig decimal rather than pure decimal. Thus, the decimal inallv read into the register. While the novel and distinctive features of the inven explicitlynumber 0.328.125 expressed in as binary coded decimal form can be 60 tion are particularly pointed out in the appended claims, a more expository treatment of the invention, in principle (0x23-1-0x22--1 X21--1 X20) 10-1-- (0x23 and in detail, together with additional objects and advan --0x22--1 X21--0x20) 10-2-(1x23-1-0x22 tages thereof, is afforded by the following description --0x21--0x20) 10-3-1-(0x23-1-0x22--0X21 and accompanying drawings in which: --1x20) 10-4--(0x23--0x22-1-1 X21 65 FIG. 1 is a block diagram of the conversion apparatus; --0x20) 10-5--(0x23-1X22-1-0x21--1x20) 10-6 FIG. 2 is a block diagram of the logic circuitry em More briefly, this number is commonly written as bodied in each of the diode matrices shown in FIG. 1; FIG. 3 is a chart illustrating the operation of the ap 0000.001 1 0010 1000 0001 0010 0 101. It will be noted paratus of FIGS.
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