Draw the truth table for a $2-$input NAND gate.

Which gate has the following truth table.

$\backslash$table$[[x,Y,$Output$],[0,0,1],[0,1,0],[1,0,0],[1,1,1]]$

Simplify the following expression using the rules:

$a^{\text{'}}{b}^{\text{'}}cd+a{b}^{\text{'}}bcd+a{b}^{\text{'}}cd+ab{c}^{\text{'}}{d}^{\text{'}}+ab{c}^{\text{'}}d+abc{d}^{\text{'}}+$abcd

Simplify the following expression with K$-$Map:

$x\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar(C)D\frac{+}{b}ar(A)BCD\frac{+}{b}ar\frac{A}{b}ar(B)CD\frac{+}{b}ar(A)\frac{B}{b}ar(C)D$

Simplify the following expression with K$-$Map: