Digital Systems

Just another WordPress.com weblog

Implications of DeMorgan’s Theorems

Let us examine these teorems (16) and (17) from the standpoint of logic circuits. First, consider theorem (16),

X + y =x.y

The left-hand side of the equation can be viewed as the output of a NOR gate whose inputs are x and y. The right-hand side of the equation, on the other hand, is the result of first inverting both x and y and then putting them through an AND gate. These two representations are equivalent and illustrated in Figure 3-26(a).

Figure 3-26 (a) Equivalent circuits implied by theorem (16); (b)alternative symbol for the NOR function.

Symbol for the NOR function

Figure 3-27 (a) Equivalent circuits implied by theorem (17); (b) alternative symbol for the NAND function.

symbol for the NAND function.

What this means is that an AND gate with INVERTERs on each of its inputs is equivalent to a NOR gate. In fact, both representations are used to represent the NOR function. When the AND gate with inverted inputs is used to represent the NOR function, it is usually drawn as shown in Figure 3-26(b), where the small circles on the inputs represent the inversion operation.

Now consider theorem (17),

X.Y=X+Y

The left side of the equation can be implemented by a NAND gate with inputs x and y. The right side can be implemented by first inverting inputs x and y and then putting them through an OR gate. These two equivalent representations are shown in Figure 3-27(a). The OR gate with INVERTERs on each of its inputs is equivalent to the NAND gate. In fact, both representations are used to represent the NAND function. When the OR gate with inverted inputs is used to represent the NAND function, it is usually drawn as shown in Figure 3-27(b), where the circles again represent inversion.

 

November 9, 2007 - Posted by | Digital Systems

Tiada komen.

Tinggalkan Jawapan

Masukkan butiran anda dibawah atau klik ikon untuk log masuk akaun:

WordPress.com Logo

Anda sedang menulis komen melalui akaun WordPress.com anda. Log Out / Tukar )

Twitter picture

Anda sedang menulis komen melalui akaun Twitter anda. Log Out / Tukar )

Facebook photo

Anda sedang menulis komen melalui akaun Facebook anda. Log Out / Tukar )

Google+ photo

Anda sedang menulis komen melalui akaun Google+ anda. Log Out / Tukar )

Connecting to %s

%d bloggers like this: