How to resolve the algorithm Non-decimal radices/Convert step by step in the ALGOL W programming language
How to resolve the algorithm Non-decimal radices/Convert step by step in the ALGOL W programming language
Table of Contents
Problem Statement
Number base conversion is when you express a stored integer in an integer base, such as in octal (base 8) or binary (base 2). It also is involved when you take a string representing a number in a given base and convert it to the stored integer form. Normally, a stored integer is in binary, but that's typically invisible to the user, who normally enters or sees stored integers as decimal.
Write a function (or identify the built-in function) which is passed a non-negative integer to convert, and another integer representing the base. It should return a string containing the digits of the resulting number, without leading zeros except for the number 0 itself. For the digits beyond 9, one should use the lowercase English alphabet, where the digit a = 9+1, b = a+1, etc. For example: the decimal number 26 expressed in base 16 would be 1a. Write a second function which is passed a string and an integer base, and it returns an integer representing that string interpreted in that base. The programs may be limited by the word size or other such constraint of a given language. There is no need to do error checking for negatives, bases less than 2, or inappropriate digits.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Non-decimal radices/Convert step by step in the ALGOL W programming language
Source code in the algol programming language
begin
% returns with numberInBase set to the number n converted to a string in %
% the specified base. Number must be non-negative and base must be in %
% range 2 to 36 %
procedure convertToBase( integer value n
; integer value base
; string(32) result numberInBase
) ;
begin
string(36) baseDigits;
integer val, strPos;
assert( n >= 0 and base >= 2 and base <= 36 );
baseDigits := "0123456789abcdefghijklmnopqrstuvwxyz";
numberInBase := " ";
val := n;
strPos := 31;
while
begin
% a(b//c) is the substring of a starting at b with length c. %
% The first character is at position 0. The length must be %
% an integer literal so it is known at compile time. %
numberInBase( strPos // 1 ) := baseDigits( val rem base // 1 );
val := val div base;
strPos := strPos - 1;
val > 0
end
do begin end
end convertToBase ;
% returns the string numberInBase converted to an integer assuming %
% numberInBase ia a string in the specified base %
% base must be in range 2 to 36, invalid digits will cause the program %
% to crash, spaces are ignored %
integer procedure convertFromBase( string(32) value numberInBase
; integer value base
) ;
begin
string(36) baseDigits;
integer val, cPos;
assert( base >= 2 and base <= 36 );
baseDigits := "0123456789abcdefghijklmnopqrstuvwxyz";
val := 0;
for strPos := 0 until 31 do begin
string(1) c;
c := numberInBase( strPos // 1 );
if c not = " " then begin
cPos := 0;
while baseDigits( cPos // 1 ) not = c do cPos := cPos + 1;
val := ( val * base ) + cPos;
end
end;
val
end convertFromBase ;
% test the procedures %
string(32) baseNumber;
i_w := 3; % set integer output width %
for i := 2 until 36 do begin
convertToBase( 35, i, baseNumber );
write( 35, i, baseNumber, " ", convertFromBase( baseNumber, i ) );
end
end.
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