Question

1. Consider the function $f = a(b + \bar{d}) + \bar{a}(\bar{c}(b \oplus d) + bcd)$. (a) Find the sum-of-product expression for $f$ with as few literals as possible. \begin{tabular}{|l|c|c|c|} \hline Gate & Number of Transistors & $t_{cd}$ & $t_{pd}$ \\ \hline NOT & 2 & 0.4 & 0.5 \\ AND2 & 6 & 2.2 & 2.6 \\ OR2 & 6 & 2.2 & 2.6 \\ NAND2 & 4 & 1.8 & 2.1 \\ NOR2 & 4 & 1.8 & 2.1 \\ XOR2 & 8 & 2.6 & 3.2 \\ XNOR2 & 8 & 2.6 & 3.2 \\ \hline \end{tabular} (b) Give an implementation of $f$ that minimizes, in order of highest to lowest priority, the number of transistors, the critical path length, and then the short path length. Only use the gates listed in the gate table.

          1. Consider the function $f = a(b + \bar{d}) + \bar{a}(\bar{c}(b \oplus d) + bcd)$. 
(a) Find the sum-of-product expression for $f$ with as few literals as possible.
\begin{tabular}{|l|c|c|c|}
\hline
Gate & Number of Transistors & $t_{cd}$ & $t_{pd}$ \\
\hline
NOT & 2 & 0.4 & 0.5 \\
AND2 & 6 & 2.2 & 2.6 \\
OR2 & 6 & 2.2 & 2.6 \\
NAND2 & 4 & 1.8 & 2.1 \\
NOR2 & 4 & 1.8 & 2.1 \\
XOR2 & 8 & 2.6 & 3.2 \\
XNOR2 & 8 & 2.6 & 3.2 \\
\hline
\end{tabular}
(b) Give an implementation of $f$ that minimizes, in order of highest to lowest priority, the number of
transistors, the critical path length, and then the short path length. Only use the gates listed in the
gate table.

1. Consider the function f = a(b + d̅) + a̅(c̅(b ⊕ d) + bcd).
(a) Find the sum-of-product expression for f with as few literals as possible.

Gate Number of Transistors tcd tpd

NOT 2 0.4 0.5

AND2 6 2.2 2.6

OR2 6 2.2 2.6

NAND2 4 1.8 2.1

NOR2 4 1.8 2.1

XOR2 8 2.6 3.2

XNOR2 8 2.6 3.2

(b) Give an implementation of f that minimizes, in order of highest to lowest priority, the number of
transistors, the critical path length, and then the short path length. Only use the gates listed in the
gate table.

Added by Patricia C.

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