Digital Circuits & Design, 1st Education by Pearson

4.12 | Chapter 4

=+++ +=AB AC BC AA AA()

()

∵ 1

=+++AB AC ABCABC

=+ ++()

()

AB ABCACABC

=+++ += +=AB CACB

BC

() () (,)11 11

11

∵

=+

AB AC

4.2.14 | De Morgan’s Theorem-I

NOR logic is equivalent to AND logic with inverted inputs. De Morgan’s rst law is stated

below:

AB

AB

+= ⋅ (4.27)

Logic diagram of Eq. (4.27) is given in Figure 4.20 and its truth table is given in Table 4.15.

A

B

X = A + BX = AB

B

A

X =

AB

B

A

FIGURE 4.20 | De Morgan’s theorem-I

TABLE 4.15 | De Morgan’s rst law

Inputs Intermediate Outputs Outputs

A B A+B

A

B

AB+

AB

0 0 0 1 1 1 1

0 1 1 1 0 0 0

1 0 1 0 1 0 0

1 1 1 0 0 0 0

4.2.15 | De Morgan’s Theorem-II

NAND logic is equivalent to ...