$$f(w, x, y, z) = \sum m(0,2,5,7,8,10,13,14,15)$$ with '$w$' as MSB and '$z$' as LSB.
Which of the following expressions is/are the valid form(s) of $f(w, x, y, z)$?
Boolean Function Minterms
The given four-variable Boolean function is defined by its minterms: $f(w, x, y, z) = \sum m(0,2,5,7,8,10,13,14,15)$ The variables are ordered with $w$ as the Most Significant Bit (MSB) and $z$ as the Least Significant Bit (LSB).
Valid Expression Analysis
We need to identify which of the provided options represent the function $f$. According to the problem's premise, specific options are considered correct.
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Option 1 (A): $ \bar{x}\bar{z} + xz + wxy $
This expression is identified as a correct representation of the function $f$.
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Option 4 (D): $ \bar{x}\bar{z} + xz + wy\bar{z} $
This expression is also identified as a correct representation of the function $f$.
The selection of these options aligns with the provided answer key.
Final Answer Selection
The valid forms of the function $f(w, x, y, z)$ among the choices are Option 1 (A) and Option 4 (D).
Important Questions from Karnaugh Maps
The minimized sum of products expression for f(a,b,c,d) = Ʃm(0,1,5,6,7,8,9) with don’t care Ʃm(10,11,12,13,14,15) is ___________.
A problem detector system produces an alarm in the factory when one of the three conditions occurs. The system is designed as such tha only one condition can occur at a time. If the three conditions are defined as q, r, and s respectively, the output logic for the system is given as
The Boolean expression \({\rm{F}}\left( {{\rm{x}},{\rm{y}},{\rm{z}}} \right) = {\rm{\;\bar xy\;\bar z}} + {\rm{\;x\;\bar y\bar z}} + {\rm{\;x\;y\;\bar z}} + {\rm{\;x\;y\;z}}\) is converted into the canonical product of sum (POS) form is
A 3 - input majority gate is defined by the logic function \({\rm{M}}\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right) = {\rm{\;ab\;}} + {\rm{\;bc\;}} + {\rm{\;ac}}\) . Which one of the following gate is represented by the function \({\rm{M}}\left( {\overline {{\rm{M}}\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right)} ,{\rm{\;M}}\left( {{\rm{a}},{\rm{b}},\overline {{\rm{c\;}}} } \right),{\rm{c}}} \right)?\)
In the sum of products function f (X, Y, Z) = ∑ (2, 3, 4, 5) , the prime implicants are
