1. Opis zadanego układu w postaci sumującej i iloczynowej i realizacja za pomocą bramek AND i OR:

-Opis układu w postaci sumującej :

$$OUT = \sum_{}^{}{(0,4,5\left( 2 \right))}$$

$$OUT = \overset{\overline{}}{A}*\overset{\overline{}}{B}*\overset{\overline{}}{C} + A*\overset{\overline{}}{B}*\overset{\overline{}}{C} + A*\overset{\overline{}}{B}*C$$

-Schemat układu :

-Opis w postaci iloczynowej:

$$OUT = \prod_{}^{}{(1,3,6,7\left( 2 \right))}$$

$$OUT = \left( A + B + \overset{\overline{}}{C} \right)*\left( A + \overset{\overline{}}{B} + \overset{\overline{}}{C} \right)*\left( \overset{\overline{}}{A}*\overset{\overline{}}{B}*C \right)*(\overset{\overline{}}{A} + \overset{\overline{}}{B} + \overset{\overline{}}{C})$$

-Schemat układu :

2. Postaci zminimalizowane powyższych funkcji względem 0 i 1:

-Względem 1:

$$OUT = \sum_{}^{}{(0,4,5\left( 2 \right))}$$

$$OUT = \overset{\overline{}}{A}*\overset{\overline{}}{B}*\overset{\overline{}}{C} + A*\overset{\overline{}}{B}*\overset{\overline{}}{C} + A*\overset{\overline{}}{B}*C$$

C AB	O	1
00	1	0
01	X	0
11	0	0
10	1	1

$$OUT = \overset{\overline{}}{A}*\overset{\overline{}}{C} + A*\overset{\overline{}}{B}$$

-Schemat układu :

-Względem 0:

$$OUT = \prod_{}^{}{(1,3,6,7\left( 2 \right))}$$

$$Out = \left( A + B + \overset{\overline{}}{C} \right)*\left( A + \overset{\overline{}}{B} + \overset{\overline{}}{C} \right)*\left( \overset{\overline{}}{A}*\overset{\overline{}}{B}*C \right)*(\overset{\overline{}}{A} + \overset{\overline{}}{B} + \overset{\overline{}}{C})$$

C AB	O	1
00	1	0
01	X	0
11	0	0
10	1	1

$$OUT = (A + \overset{\overline{}}{C})*(\overset{\overline{}}{B})$$

3.Realizacja funkcji na bramkach NOR w postaci pełnej i zminimalizowanej :

- W postaci pełnej :

$$OUT = \prod_{}^{}{(1,3,6,7\left( 2 \right))}$$

$$OUT = \left( A + B + \overset{\overline{}}{C} \right)*\left( A + \overset{\overline{}}{B} + \overset{\overline{}}{C} \right)*\left( \overset{\overline{}}{A}*\overset{\overline{}}{B}*C \right)*(\overset{\overline{}}{A} + \overset{\overline{}}{B} + \overset{\overline{}}{C})$$

$$\overset{\overline{}}{a}*\overset{\overline{}}{b} = \overset{\overline{}}{a + b}$$

$$OUT = \overset{}{\left( A + B + \overset{\overline{}}{C} \right)*\left( A + \overset{\overline{}}{B} + \overset{\overline{}}{C} \right)*\left( \overset{\overline{}}{A}*\overset{\overline{}}{B}*C \right)*(\overset{\overline{}}{A} + \overset{\overline{}}{B} + \overset{\overline{}}{C})}$$

$$OUT = \overset{\overline{}}{\overset{\overline{}}{\left( A + B + \overset{\overline{}}{C} \right)} + \overset{\overline{}}{\left( A + \overset{\overline{}}{B} + \overset{\overline{}}{C} \right)} + \overset{\overline{}}{\left( \overset{\overline{}}{A}*\overset{\overline{}}{B}*C \right)} + \overset{\overline{}}{(\overset{\overline{}}{A} + \overset{\overline{}}{B} + \overset{\overline{}}{C})}}$$

-W postaci zminimalizowanej :

$$OUT = \prod_{}^{}{(1,3,6,7\left( 2 \right))}$$

$$OUT = (\overset{\overline{}}{A} + \overset{\overline{}}{C})*(\overset{\overline{}}{B})$$

$$OUT = \overset{\overline{}}{\overset{\overline{}}{(A + \overset{\overline{}}{C})*(\overset{\overline{}}{B})}} = \overset{\overline{}}{\overset{\overline{}}{(A + \overset{\overline{}}{C})} + \overset{\overline{}}{(\overset{\overline{}}{B})}}$$