The binary number system was refined by Gottfried Wilhelm Leibniz(published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it

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An advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation caused by noise. For example, a continuous audio signal transmitted as a sequence of 1s and 0s, can be reconstructed

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A digital circuit is typically constructed from small electronic circuits called logic gates that can be used to create combinational logic.

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Engineers use many methods to minimize logic redundancyin order to reduce the circuit complexity. Reduced complexity reduces component count and potential errors and therefore

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In 2009, researchers discovered that memristors can implement a boolean state storage (similar to a flip flop, implication and logical inversion), providing a complete logic family with

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• Boolean algebra
• Combinational logic
• De Morgan's laws

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Digital design started with relay logic which is relatively inexpensive and reliable, but slow. Occasionally a mechanical failure would occur. Fan-outs were typically about 10, limited by the resistance of the coils and arcing on the contacts from high voltages.

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