What type of expression is [latex]Y=(\overline{A} +B)·(A+\overline{B} )[/latex], what sum terms are included in it, and what is its expanded form?

This is a product of sums expression, with two sum terms,[latex](\overline{A} +B)[/latex] and [latex](A+\overline{B} )[/latex]. Using Boolean algebra: [latex](\overline{A} +B)·(A+\overline{B} )=(\overline{A} +B)·A+(\overline{A} +B)·\overline{B}[/latex] distributive law [latex] =\overline{A} ·A+B·A+\overline{A}· \overline{B} +B· \overline{B} [/latex] distributive law [latex] =\overline{A}· \overline{B} +A·B[/latex] Equation 1.3: [latex]A\cdot \overline{A}=0[/latex] (This is the Boolean expression for the exclusive-NOR gate discussed in the next section.)

Question 1.15: What type of expression is Y=(A+B)·(A+B), what sum terms are...

Introduction to Digital Electronics [EXP-30805]

What type of expression is $Y=(\overline{A} +B)·(A+\overline{B} )$ , what sum terms are included in it, and what is its expanded form?

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This is a product of sums expression, with two sum terms, $(\overline{A} +B)$ and $(A+\overline{B} )$ .

Using Boolean algebra:

$(\overline{A} +B)·(A+\overline{B} )=(\overline{A} +B)·A+(\overline{A} +B)·\overline{B}$ distributive law

$=\overline{A} ·A+B·A+\overline{A}· \overline{B} +B· \overline{B}$ distributive law

$=\overline{A}· \overline{B} +A·B$ Equation 1.3: $A\cdot \overline{A}=0$

(This is the Boolean expression for the exclusive-NOR gate discussed in the next section.)