Conversion to Binary and IEEE-754 Binary

[Eddie W. Shore]

Here is my second attempt at it, except I just concentrated at the conversion to binary, with a user-given precision level.

To help with rounding the number, I first round the number to the nearest 1/2^n, then convert the result to binary.

I have not retried the IEEE-754 yet.

The program RBIN converts any real number in base 10 to base 2, including non-integers and negative numbers. The result is displayed as a string.

RBIN will need two arguments: the number to be converted and the precision level.

For the precision level:

1 rounds the number to the nearest 1/2 before conversion.

2 rounds the number to the nearest 1/4 before conversion.

3 rounds the number to the nearest 1/8 before conversion.

4 rounds the number to the nearest 1/16 before conversion.

and so on.

HP Prime Program: RBIN

Code:

EXPORT RBIN(x,p)
BEGIN
// 2020-07-11 EWS
// Decimal to Binary
// decimal, precision
// for real x, rounded 1/2^p

LOCAL b,i,f,n,s,w,k,str;
s:=ABS(x);
b:=IP(s)+ROUND(FP(s)*2^p,0)/2^p;
str:="";
i:=IP(b);
f:=FP(b);

IF i≠0 THEN
n:=IP(LOG(i)/LOG(2));
FOR k FROM n DOWNTO 0 STEP 1 DO
w:=IP(i/2^k);
str:=str+STRING(w);
i:=i-w*2^k; 
END;
END;

IF f≠0 THEN
str:=str+".";
FOR k FROM 0 TO p-1 DO
w:=IP(2*f);
str:=str+STRING(w);
f:=FP(2*f);
END;
END;

IF x<0 THEN
str:="-"+str;
END;

RETURN str;
END;

Examples:

RBIN(-0.985,3) returns "-1"
RBIN(-0.985,6) returns "-.111111"
RBIN(-0.985,9) returns "-.111111000"

RBIN(860.63,3) returns "1101011100.101"
RBIN(860.63,6) returns "1101011100.101000"
RBIN(860.63,9) returns "1101011100.101000011"


Link: http://edspi31415.blogspot.com/2020/08/h...sions.html