$$\mathop {\underline x }\limits^ \bullet = \left[ 2 \right]\underline x + \left[ 1 \right]u;\underline y = \left[ {\matrix{ 1 & 2 \cr } } \right]x$$

$$\mathop {\underline x }\limits^ \bullet = \left[ { - 2} \right]\underline x + \left[ 1 \right]u;\underline y = \left[ {\matrix{ 1 \cr 2 \cr } } \right]x$$

$$\mathop {\underline x }\limits^ \bullet = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 2} \cr } } \right]\underline x + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u;\underline y = \left[ {\matrix{ 1 & 2 \cr } } \right]x$$

$$\mathop {\underline x }\limits^ \bullet = \left[ {\matrix{ 2 & 0 \cr 0 & 2 \cr } } \right]\underline x + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u;\underline y = \left[ {\matrix{ 1 \cr 2 \cr } } \right]x$$

F= AND (P, Q)

F= OR (P, Q)

F= XNOR (P, Q)

F= XOR (P, Q)

changed from 0 to 1

changed from 1 to 0

changed in either direction

not changed

$${D_A} = {Q_{B,}}\,{D_B} = {Q_A}$$

$${D_A} = {\overline Q _A},\,{D_B} = {\overline Q _B}$$

$${D_A} = \left( {{Q_A}\,{{\overline Q }_B}\, + {{\overline Q }_A}\,{Q_B}} \right),\,\,{D_B} = {Q_A}$$

$${D_A} = \left( {{Q_A}{Q_B} + {{\overline Q }_A}{{\overline Q }_B}} \right),\,\,{D_B} = {\overline Q _B}$$