Facebook
Google
GitHub
LinkedinDigital Circuits
Boolean Algebra
67 questions By Tony R. Kuphaldt
-
Question 58 of 67
An Exclusive-OR gate has the following Boolean expression:
$$A\overline{B} + \overline{A}B$$
Draw the schematic diagram for a gate circuit exhibiting this Boolean function, constructed entirely from NAND gates.
Reveal answer
Notes:An interesting feature of this circuit is the final three NAND gates: two NAND gates feeding into a third NAND gate is equivalent to two AND gates feeding into an OR gate, thanks to DeMorgan’s Theorem!
-
Question 59 of 67
An automobile manufacturer needs a logic circuit to perform a specific task in its new line of cars. These cars will be equipped with a “headlight left on” alarm that sounds any time these two conditions are met: headlights on and ignition switch off. Draw the schematic diagram of a logic gate circuit that will implement this alarm, constructed entirely out of NAND gates.
Reveal answer
Follow-up question: suppose the alarm unit required more current than the final NAND gate could source. Add a transistor “buffer” stage to the logic gate circuit to drive additional current to the alarm.
Challenge question: explain how the following NOR gate circuit performs the exact same logic function with fewer components:
Notes:This question is a really good one to ask your students how they arrived at a solution. It is easy enough to simply look at the given answer and repeat it, but of course the intent of this question is to get students to think how they might design such a circuit completely on their own.
-
Question 60 of 67
Draw a schematic for a logic gate circuit using nothing but two-input NOR gates that mimics the operation of this relay circuit:
Reveal answer
Follow-up question: note the manner in which NOR gates are used as inverters in this circuit. Compare this against the following (alternative) method:
Are there any distinct advantages you see to either method?
Notes:In my very first technical job, I worked as a CNC maintenance technician in a small machine shop, maintaining computer-controlled machine tools such as mills and lathes. A really neat project I got to work on at that job was the conversion of a 1970’s era American-made machine tool to modern Japanese computer control. A lot of logic in that old machine tool was implemented using relays, and we replaced the cabinets full of relays with solid-state logic in the Japanese control computer. Actually, the solid state logic was a programmable logic controller or PLC function inside the Japanese control computer rather than discrete semiconductor logic gates. However, we very well could have replaced relays with hard-wired gates. The purpose of this question, if you haven’t guessed by now, is to familiarize students with the concept of replacing electromechanical relays with semiconductor logic gates, especially identical logic gates such as NOR gates which are “universal.”
Question 29, answer 3 has a typo - should be A*B + !(D)*E not A*B+!(D*E)