SU1302438A1 - Position code converter from one number system to another - Google Patents

Abstract

The invention relates to the field of computer technology and can be used in the construction of converters of codes of numbers from one number system to another. The aim of the invention is to extend the functionality by providing a reverse ko conversion, - and with any base into a code with another base. The goal is achieved by the fact that in a position code converter from one number system to another, containing scalers adders 1, connected to a triangular matrix, each scaling adder contains multiplier 7 and adder 8, the first input of which is connected to the output of the multiplier, and the second one with the output of the neighboring junior scaling adder. 1 il. SL

Description

The invention relates to computing and can be used in the construction of converters of codes of integers from one number system to another.

The aim of the invention is to enhance the functionality of the converter by providing a reverse conversion of a code with one base into a code with a different basis.

The drawing shows a block diagram of a four-bit converter.

The converter contains scaling adders 1 connected in a triangular matrix, each of which has an input 2 high order, input 3 low order, output 4 high order and output 5 low order, control input 6 and contains a multiplier 7 and adder 8. In addition, the converter has bits of inputs 9, output 10 of the operation mode selection and outputs 11,

If it is necessary to emphasize the use of a number as a digit, the sign C is used (for example, DD is a hexadecimal digit or some other number system. If it is not necessary to emphasize in which number system the number is written, the number record is indexed by the base system enclosed in brackets (for example , 2S tLS number written in hexadecimal notation.

Let the converter be used to convert integers and a number system with base S to a number system with base R and back from the R-system to S. Let us assume for definiteness that S. R. To represent the S-digit in the R-number system, it suffices R-digit.

The number of inputs 2 is equal to the number of inputs 3, is equal to the number of outputs 4 and the number of outputs 5 of the scaling adder 1 and is equal to t, the number of outputs of the adder 8 is equal to 2m. When converting a number from the S-number system to R by

The input 2 of the second adder 1 of the first row of the matrix receives the number b, and the input 3 of this adder 1 - the number a, At the outputs 4 and 5 of the adder 1 appears the number (+ a). And the highest digit appears at course 4, and the youngest at output 5 of the wagon train begins the highest digit of the number (b S + a

inputs 9 are not S-numbers, but S-codes

corresponding to them numbers. For example, 55 as У UG ED Gkak bt, - if S is 10, R 16, then w 2 six- .p are ad-hatch digits, P,. .., Similarly, at output 4 arbitrarily correspond to the same single i-ro (where) scaling parameters, which, in turn, of the first row coding adder 1 of the first row are matched with two decimal digits, that is,

 00,

 01, etc. before

  15 (the sign replaces the word matches), and when converting a decimal number to hexadecimal, the inputs 9 are not decimal digits 0.1, .., 9, but pairs of decimal numbers 00, 01, 02,. ,,, 09 .

When translating a (k + 1) -digit number N from an S-number system to R, the converter works as follows,

At the input 10 of the control is fed a lo (or 1), with this conical O

multiplier 7, equal to S, multiplier 7 and adder 8 operate in the R-numbering system, but the results at their outputs appear as S-codes of R-digits. Denote the S-digits of the input number N as a, ,,., , a, (where a is the highest digit; a is the youngest), then

A. S

 (.., ((+ a.,) -S +

N a

. + a

: -2 s: l

thirty

45

The input 2 of the first scaling adder 1 of the first row of the matrix receives the number a, and the input 3 of this 3 rd matrix 1 receives the number a, the outputs 4 and 5 of which contain the number (+ a,) presented in the R-number system with two S- codes R-diff. In this case, the highest R-digit of the number (35 a) appears at output 4, and the lowest R-number at output 5 of this adder 1.

Denote the high and low R-digits of the number (+) of the first element of the first row of the matrix as b .. and

40

 K-1 - k.

. (2)

Since S R, the R-digit b will also be an S-digit, and the R-digit b may or may not be an S-digit,

The input 2 of the second adder 1 of the first row of the matrix receives the number b, and the input 3 of this adder 1 - the number a, At the outputs 4 and 5 of the adder 1 appears the number (+ a). And the highest digit appears at output 4, and the youngest appears at output 5. Denote the highest digit of the number (b S + a)

how bg ed bk, bt, - .р - Similarly, at output 4 of an arbitrary i-ro (where) scaling adder 1, the first row of the matrix appears R-digit b is also an S-digit, and 5 of this adder 1 appears in an R-digit, and the yotor is determined by the equality

13

which

Bk .- (- 1- (,

S + a

The output 5 of the last k-ro adder 1 of the first row of the matrix is Vits

Logic 1 (or O, respectively) is fed to input 10. Wherein

The R-digit that defines the expression, the 0 constant multiplied by multiplier 7 is equal to R, a multiplier 7 and adder 8 work in (I) S-number system /

by

H + b, - R,

where b, 1 is the r-digit, shown on output 4 of this k-ro adder 1 of the first row of the matrix or

S + a) S + S + ..... + a) S +

S + b ..) S +

b, (... ((a + aj- R (... ((b

Bk- )

S +,

The multiplier 7 is equal to R, a multiplier 7 and adder 8 operate in (I) S-number system /

The breakdown of the outputs of the adder 8 into f, 15 two groups of m is essentially a translation of the S-number appearing at the output of the adder 8 into the T-system (T s), with the T-digits being encoded S-digits. We can assume that the adder 8 (and the multiplier 7 together with it) work in the T-number system, but therefore the operation of the converter when converting a number from a system with a smaller base to

20

, ...,

k - + b,) - S + b,.

(five)

In formula (5), the decrease is equal to the input number N, and the deductible is equal to

the number of R desytkov contained in the number-25 system with a large base occurs as described.

Consider the operation of a four-digit decimal transformer into a letter M. Because there are R-digits. hexadecimal and back .. In this b b, ..., b are also S-numerals, the entry of the number M in the S-number system is

LeN multiplied by R. Thus, the .R-digit of b is equal to the number of R units, containing them in the number N. We denote the computation,,. As hexadecimal digits, two-digit decimal numbers are used; ≤ 00, -01, ..., 15.

M.Jb ,,

. , b. (6)

The size of the number M in the S-number system is one less than the size of the original number N, and the digits of the number M are fed to the scaling adders 1 of the second row of the matrix containing (k - 1) the adder 1 exactly the same as the digits of the number N subusus elements of the first row of the matrix. Repeating the same reasoning for the number M and the second row of the matrix, it is found that at the output 5 of the last element of the second row of the matrix, the R-digit of the R-tenths containing N is formed, and at the output of 4

At the outputs of 4 elements of the first row of the matrix, in vc decimal codes 02, 04, and 02Г. At output 5 of the last element of the first row of the matrix, the decimal code 03 sixteen is in

the second row of the matrix is formed

S-representation of the number of R-hundreds, containing the digits of the hexadecimal number

among the N, etc. to the last units, contained in the number 3875, ;;,

matrix rows. S-number

output 4 single element

The last row of the matrix will be an R-digit and its further conversion 55 of the ice member of the second row of the matrix requires. There is a decimal code 02. Accordingly, on output 4 elements 1 of the last row of the matrix and at the outputs 5 last elements of all

Respectively, at the outputs of the 4-elements of the second row of the matrix, in VTS decimal codes 01 and 05, at output 5, according to output 4 of the elements of the last row of the matrix, the decimal code 00, at output 5 of which

24384

The rows of the matrix form the R-representation of the original number supplied to the converter in the S-number system.

When translating a (k + 1) -digit number L from an R-number system to an S-npe-generator, it works as follows.

Logic 1 (or O, respectively) is fed to input 10. Wherein

0 constant, which produces the mind

The multiplier 7 is equal to R, a multiplier 7 and the adder 8 operate in the S-number system /

The breakdown of the outputs of the adder 8 into 15 two groups of m each is essentially a translation of the S-number appearing at the output of the adder 8 into the T-system (T s), with the T-digits being encoded S-digits. We can assume that the adder 8 (and the multiplier 7 together with it) work in the T-number system, but therefore the operation of the converter when converting a number from a system with a smaller base to

20

Consider the operation of a four-digit decimal number into hexadecimal and vice versa ..

five

0

five

In the case of,., two-digit decimal numbers are used as hexadecimal digits; ≤ 00, -01, ..., 15.

When converting a number from the decimal number system to the hexadecimal number, logical O is fed to the input 10. In this case, the constant multiplied by the multiplier 7 is 10, and the multiplier 7 and the adder 8 will work in the hexadecimal number system.

A decimal number, for example, 3875 p is translated as follows.

At the outputs of 4 elements of the first row of the matrix, in vc decimal codes 02, 04, and 02Г. At output 5 of the last element of the first row of the matrix, the decimal code 03 sixteen is in

units, contained in the number 3875, ;;,

Respectively, at the outputs of the 4-elements of the second row of the matrix, the decimal codes 01 and 05 are outputted at output 5, the full code of 02 is the decimal code 02. Respectively, at exit 4 of the last row of the matrix, the decimal code 00 appears, at output 5 of which

the decimal code is 15. The decimal code 00, which appeared at the output 4 elements of the last row of the matrix, corresponds to the number of hexadecimal thousand. Thus, a hexadecimal representation is obtained

3875 ,, „, 00

15 02 03

(7)

When converting a number from a hexadecimal number system to decimal, input 10 is supplied with logical 1. In this case, the constant multiplied by multiplier 7 is 16, and Multiplier 7 and adder 8 will work, in the decimal number system.

Hexadecimal number translation

for example, before LH .02. . OZ, - - 16 exists as follows.

The outputs of 4 elements of the first row of the matrix are decimal codes 01., 12, and 00, the output 5 of the last element of the first row of the matrix contains the decimal code of the figure 35, At the outputs of 4 elements of the second row of the matrix clocks The primary codes are 00 and 04, at the output 5 of the last element of the second row of the matrix, the decimal iodine of the digit 48, the output 4 and 5 of the last row element. The matrices are in decimal codes 00 and 04. Thus

SUMS

Go044835:; oG -String ha ha ha ta ha ha ha ta ha I b Hm H H H H H H Th H. ± .... 1- ± -1

149

О 1 О О 1 О 1 О .1 О 1 О 1 1 1 1 1 Filling in the entire table, get the table task of the system of functions. V. This table includes all possible sets of arguments aa, ..., a.

It is more rational, but not necessary, to perform the required device based on ROM, for example, with organization 9–8.

The second half of the ROM volume is reserved for a device that works when converting binary numbers to binary digits. In this case, one is fed to input 6. ROM memory is used most rationally if you convert a binary

five

When converting binary-decimal numbers to binary S 10, R 2, m 4. The multiplication factor of multiplier 7 is 10, - multiplier 7 and adder 8 operate in a binary number system. In order to design a scaling adder 1, it is necessary to define a system of logical functions in tabular form. We denote the junior input 3 a, a, a „, a. Similarly, we denote the input, a ,,, a, a and a, and input 6 as a. In the same way we denote the output 5 b, b

- 4 b

l

and b

b, ib

exit 4

The table that defines this system of functions contains 256 rows and .17 columns. In the first nine columns, the values of the arguments a, a, ..., a, and in the remaining eight columns of Zach are written the values of the functions C, b, ..., bo ,. Since, when converting binary-decimal numbers to binary, input 6 of the correction element 1 is zero, the value of the argument a is always zero in the compiled table. Let us number the rows of the table from O to 255. Consider the sets of variables and as four-bit binary numbers, find the eighth bit binary number, determined by the formula

Yom Yom, ,,,,

and write down the values of bits of this number in columns, ..., Bd in the row with the binary number. a e S, a, a, a, a

five

n 1/0 i 3e3s & 5 a “S S“

For example, line 149 of the table being compiled looks as follows:

number in binary-octal, and then translate it into binary-decimal.

First, the binary number is split into triads, starting with the least significant bit, and then each triad is supplemented to the tetrad by adding a zero high order to it. This conversion is carried out by external installation of the inputs 9.

Thus, when converting a binary-octal number to a binary-decimal S 8,, R Ipj.m 1, i.e. inputs 2 and 3 and outputs 4.5 consist of four binary bits. The multiplication factor of 7 is 8,

multiplier 7 and adder 8 operate in a decimal number system. To design a scaling adder, a similar table is created. Indicate binary bits of 3 inputs and a, starting with the highest,

as

aza. and

and binary bits of input 2 as aa a and a, binary bits of output 5 as

yes 4

and b,

binary bits output and b respectively. The table has seventeen columns. Filling the table

one hundred lines

worn out in the following way.

Number the rows of the table with two-digit decimal numbers from 00 to

 I j i i l i l i j i kbiji a

67

101 1001 1 101010101

Filling the entire table, get a table assignment of functions. On non-entered into the table sets of arguments, functions can take arbitrary values.

The proposed device can also be realized on the basis of the ROM with the organization, and for its implementation half of the volume of the ROM is required. ., Q

Combining both the compiled tables into one, get the complete ROM programming table to work as a scaling adder in the integer converter, designed to convert binary-decimal numbers to binary and binary to binary-decimal.

Claims (1)

Invention Formula A position code converter from one number system to another, containing scaling adders, connected to a triangular matrix in such a way that the high-level inputs of the first scaling adder and the low-level inputs of all the scaling adders of the first row of the matrix are connected to the corresponding bit-level inputs of the converter, the high inputs the bits of all the scales of the adders of the first row, except the first, are connected to the outputs of the lower bits of the next highest scaling adder of the first troc, input of the highest bit of the first scaling adder of the i-th row 99. In the first column of the table, the corresponding. A., in all lines one is entered. The next eight columns of the table contain the binary number of the line number. For the string. having the number a I-1 bit number 1O are two ten 15  s - tio 1-1 1О -CU Then, the binary columns of the numbers 0 and a are written into the row having the number of columns corresponding to the functions. For example, line 67 of this table appears as follows: five Q five 0 Q 5 (i 2 - k - 1, where k is the number of bits of the input code) is connected to the output of the highest bit of the scaling adder (i - 1) -th row, the input of the lower bit of the j-ro scaling adder of the i-th row (j 1 - k - i) is connected to the output of the most significant bit of the (J + 1) -th scaling adder (i - 1) -th row, the input of the most significant bit of the (j + 1) -th scaling adder of the i-th line is connected to the output of the least significant one bit j-ro of the scaling adder of the i-th row, output of the highest bit of the scaling adder (k - 1) -th row and outputs of the least significant bits of the last scaling sum The tori of all rows are bit outputs of the converter, characterized by the fact that, in order to extend the functionality by providing reverse code conversion with any base to code with any other base, in it all scalable adders contain a multiplier and adder that controls the inputs which are connected to the input of the converter operation mode selection, the output of the multiplier is connected to the input of the first term of the adder, the input of the second term of which is connected to the input of the least significant bit its adder input most significant bit coupled to an input of the multiplier, the first and second groups of outputs of the adder outputs are respectively the highest and lowest bits scaling adder.