The most prominent IPA alphabet is the SAM phonetic alphabet. For each language, a subset of the IPA characters is chosen so that it covers all relevant phonetic categories for that language, and fits into the US-ASCII code table.
SAMPA has been defined for all major European languages. The SAM phonetic alphabets are described in great detail in an appendix of their own (cf. Appendix B).
For American English, the oldest computer readable phonetic alphabet one is the ARPABET. A more detailed one was KLATTBET, used in the MITALK synthesiser (with a space between each phoneme symbol), see Table A.1.
For British English (i.e. RP), the system in use at the CSTR in Edinburgh is the Machine Readable Phonetic Alphabet (MRPA), with a space between each phoneme symbol (see Table A.2).
These coding systems both restrict the alphabet to a subset of the IPA and introduce a new nomenclature for the representation of the phonetic characters.