Simplifying an 8-bit boolean expression

boolean-algebra

I am asked to find a minimum SOP implementation of a Hex to Braille code converter. Assuming my truth table is accurate, and D stands for "Don't Care", an 8-bit K-map seems impractical. Are there any other tools for hand analysis other than basic boolean algebra simplification?

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Best Answer

Tools like Logic Friday 1 or Espresso are able to minimize a truth-table with multiple outputs and don't cares.

With Logic Friday 1, your truth-table looks as follows:

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It is possible to minimize the number of product terms in different ways:

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The result is one minimized sum-of-products expression per output:

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You can turn this into a multi-level circuit of Boolean gates:

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In case you want to experiment with Karnaugh maps including don't cares, the following web application is helpful:

Karnaugh-Veitch Map, Marburg University

Note that a four-bit map is sufficient. You need one map per output.

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