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# Binary to Decimal Conversion

IP.com Disclosure Number: IPCOM000094651D
Original Publication Date: 1965-Apr-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 2 page(s) / 32K

IBM

## Related People

Schmookler, MS: AUTHOR

## Abstract

This method compensates for errors introduced in the process of converting integers from binary to binary-coded decimal using the method of fractional conversion.

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Binary to Decimal Conversion

This method compensates for errors introduced in the process of converting integers from binary to binary-coded decimal using the method of fractional conversion.

As shown at (a) an n-position Arabic number dl-dn is expressed as an m- position binary number bl-bm. The number 21, as an example, is expressed in binary as shown at (b). To convert the binary representation at (b) back to a binary-coded decimal representation utilizing the technique of fractional conversion requires that the binary integer be scaled to a fraction. This is accomplished by multiplying the binary representation of the integer 10101 by the scaling factor shown at (c).

The fractional scaling factor can only be inexactly expressed as a binary number. If a sufficient number of digits of the scaling factor is utilized in the conversion technique, conversion problems do not normally arise. However, if it is assumed that the binary adder, used to perform the multiplication process, is limited in the number of digits which it can handle, then the scaling factor must be truncated to the maximum bit length. In this particular case, assume that the maximum bit length is 7 and that the last 5 bits shown at (c) must be discarded. This introduces an error into the conversion process which results in an erroneous result.

At (d), the multiplication of the binary integer representation of 21 by the scaling factor to convert it to a fraction is shown. To convert the resultant binary fraction to a binary-coded decimal representation, the binary fraction is repeatedly multiplied by ten, 1...