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Section5.6Exercises

1

Design a function that will detect the even 4-bit integers.

Solution
2

Find a minimal sum of products (mSoP) expression for the function

\begin{align*} F(x,y,z) &= x' \cdot y' \cdot z' + x' \cdot y' \cdot z + x' \cdot y \cdot z'\\ &\quad+\ x \cdot y' \cdot z' + x \cdot y \cdot z' + x \cdot y \cdot z \end{align*} Solution
3

Find a minimal product of sums (mPoS) expression for the function

\begin{align*} F(x,y,z) &= (x + y + z) \cdot (x + y + z') \cdot (x + y' + z')\\ &\quad \cdot \ (x' + y + z) \cdot (x' + y' + z') \end{align*} Solution
4

Find a minimal product of sums (mPoS) expression for the function

\begin{align*} F(x,y,z) &= x' \cdot y' \cdot z' + x' \cdot y' \cdot z + x' \cdot y \cdot z'\\ &\quad+\ x \cdot y' \cdot z' + x \cdot y \cdot z' + x \cdot y \cdot z \end{align*} Solution
5

Show where each minterm is located with this Karnaugh map axis labeling using the notation of Figure 5.5.7.

<<SVG image is unavailable, or your browser cannot render it>>

Answer
6

Show where each minterm is located with this Karnaugh map axis labeling using the notation of Figure 5.5.7.

<<SVG image is unavailable, or your browser cannot render it>>

Answer
7

Design a logic function that detects the prime single-digit numbers. Assume that the numbers are coded in 4-bit BCD (see Section 4.6.1). The function is \(1\) for each prime number.

Solution