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(a) Expression for \$Z\$

\$Z=(B+\overline{C})A+B(C+\overline{D})+BD\$

\$Z=AB+A\overline{C}+BC+B\overline{D}+BD\$

\$Z=AB+\overline{A}C+B\$

\$Z=B+A\overline{C}\$

(b) Truth table

A B C || Z
==========
0 0 0 || 0
0 0 1 || 0
0 1 0 || 1
0 1 1 || 1
1 0 0 || 1
1 0 1 || 0
1 1 0 || 1
1 1 1 || 1

(c) Karnaugh Map

       | BC  00  01 11 10
 ------------------------
 A  0  |     0  1  1  1

    1  |     1  0  1  1

I was sure about what the last two questions (d) and (e) were asking me. Can anyone provide some guidance on how to solve these last two questions? Thank you in advance.

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You have probably learned, that you can build every logic gate using NAND gates. This is often done, because NAND gates are easy to build.

In d), the task is to rebuild this circuit, only using NAND gates.

In e) the task is to find the critical (aka the longest) path in your circuit and calculate it's propagation delay, by using the given propagation delay of single gate.

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According to DeMorgan, a NAND gate can be used to implement an OR kind of operation. Also, you can connect the two inputs of a NAND gate together and get a unary logic function. With this knowledge you can replace AND, OR, and NOT gates with one or more NAND gates connected in different ways.

Once you've done that, remove redundant gates.

Finally, assume that the delay through each NAND gate is 20 ns. What is the longest delay path from any input to the output?

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