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Summary

Digital design is based on Boolean algebra. The rules of Boolean algebra allow logical expressions to be simplified. The basic logical operators can be implemented as digital building blocks—gates. Graphical methods, such as Karnaugh maps, are suitable tools for finding the minimal forms of Boolean expressions with fewer than six variables. Larger problems can be tackled with computer-based methods. Gates have delays, which means that non-minimal forms of Boolean expressions may be needed to prevent timing problems, known as hazards. Data can be represented using sets of bits. Different types of data can be encoded to allow manipulation. Error detecting codes are used when data is transmitted over radio or other networks.

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