3a) (5pts) Simplify the following function using Karnaugh maps F(a,b,c) = abc + abc + abc + abc

Note for clarity where the apostrophe (not) applies in this notation: abc is a * b * c; a is read as: aNOT

3b) (5pts) Show that x = xy + xy using truth tables

3c) (5pts) Show that x = xy + xy using Boolean identities

3d) 35 pts. Design a circuit to implement this specification: A security robot patrols a hallway, and has four sensors, S1) a motion detector (operating on micro changes in air currents) and a S2) vision sensor (detecting movement across the visual field), and S3) a microphone to detect sound. The robot can generate these outputs:

A) Generate a warning announcement

B) Send a text msg to the human security guard

C) Connect a phone with the security guard so he/she may listen

The robot functions:

If S1 OR S2 but not both, AND NOT S3 are detected: generate a warning announcement

If S1 AND S2 but NOT S3 are detected, generate a warning announcement and send a text to the security guard

If S3 is detected, connect a phone link with the security guard

Generate a circuit using NAND/NOR/NOT to implement a solution. Start with a TT, extract a function, minimize, convert.

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