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George Boole's classic An Investigation of the Laws of Thought, published in 1854, led to the development of two closely related areas of mathematics: symbolic logic and the mathematical system called boolean algebra. Chapter i of Boole's book demonstrated how valuable the symbols and the laws of logic are in investigating how we reason in order to reach conclusions. That material will help us in studying this chapter. Until the late 1930s boolean algebra did not seem to have many useful
applications. In 1938, Claude E. Shannon, while working at the Massachusetts Institute of Technology, used boolean algebra to analyze electrical circuits, thus opening the door for a world of applications of boolean algebra. Since then, boolean algebra has played a central role in the design, analysis, and simplification of electronic devices, including digital computers.
In this chapter we will address some of the interesting problems that
boolean algebra handles well:
- Three switches for a light fixture are in a hallway. If the light is on, it can be turned off by flipping one of the switches off. On the other hand, if it is off, flipping one of the tongues turns it on. What does the circuit look like?
- Design a circuit to compute the sum of two 3-bit numbers.
- How can boolean algebra simplify a circuit while maintaining the circuit's capabilities?
- Electronic devices display digits by lighting up a maximum of seven line segments in the adjacent configuration. What kind of circuit will accept the binary-coded decimal expansion of a decimal digit and light up a segment?