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Old 03-24-2013, 09:03 AM
Oldie Offline
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Question Binary Operations

I understand that the three fundamental binary operations are the Boolean Operators, AND, OR and NOT. All other functions are built up from these three fundamentals.

This was a bit of a surprise to me when I first came across it. Then I realised that it is similar to the situation in decimal arithmetic. If you can add and subtract single digits you can build up to all arithmetic functions. Adding many digit numbers is done by breaking it down to single digit adds; Multiplication is multiple additions; raising to a power is multiple multiplications etc.

However I have never seen it stated that the basic operations are ADD and SUBTRACT. Why three for binary and apparently two for decimal? Is there not a formal statement of equivalence between the fundamental operations in an arithmetic of base M and one of base N?

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