Synthetic Programming (HP-41)
Encyclopedia
Synthetic programming is an advanced technique of programming the HP-41C range of calculators
Programmable calculator
Programmable calculators are calculators that can automatically carry out a sequence of operations under control of a stored program, much like a computer. The first programmable calculators such as the IBM CPC used punched cards or other media for program storage...

, involving creating instructions (or combinations of instructions and operands) that cannot be obtained using the standard capabilities of the calculator.

Some HP-41C instructions are coded in memory using multiple byte
Byte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...

s. Some of these sequence of bytes correspond to instructions the calculator is able to execute, but these cannot be entered in the program memory using conventional program entry methods (i.e. using the calculator as described in the user's manual.) Synthetic programming uses a bug
Software bug
A software bug is the common term used to describe an error, flaw, mistake, failure, or fault in a computer program or system that produces an incorrect or unexpected result, or causes it to behave in unintended ways. Most bugs arise from mistakes and errors made by people in either a program's...

in the calculator firmware to enter those byte sequences as a sequence of other instructions, then partially skipping halfway through the first instruction, so that the calculator believes the end of the first instruction is actually the beginning of a new one.

It is not clear if the creators behind the HP-41 were aware of all these "black holes". HP did not support officially these techniques, but probably was intrigued by the strange operations and in some cases allowed enthusiasts to practice in their offices and helped to improve it among a whole sense of curiosity. It was kept as a kind of wonder, even secret, in technical schools.
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