Table 1.

The 12 Boolean functions used and their algebraic equivalents

	Boolean function	Algebraic equivalent
1	X1 AND X2	Z1Z2
2	X1 AND $\overline{\text{X}}$2	Z1(1 - Z2)
3	$\overline{\text{X}}$1 AND X2	(1 - Z1)Z2
4	$\overline{\text{X}}$1 AND $\overline{\text{X}}$2	(1 - Z1)(1 - Z2)
5	X1	Z1
6	X2	Z2
7	$\overline{\text{X}}$1	1 - Z1
8	$\overline{\text{X}}$2	1 - Z2
9	X1 OR X2	Z1 + Z2 - Z1Z2
10	$\overline{\text{X}}$1 OR $\overline{\text{X}}$2	1 - Z1Z2
11	X1 OR $\overline{\text{X}}$2	1 - Z2 + Z1Z2
12	$\overline{\text{X}}$1 OR X2	1 - Z1 + Z1Z2