Digital Circuits

Boolean Operators:
Single Input Single Output: $A\;\rightarrow$   Operation$\;\;B$ A and B take binary (0,1) values.

eg. NOT operation 12.1. $B=\overline{A}$

Figure 12.1: A NOT gate

Multiple Inputs Single Output:

Eg 1. OR operation 12.2.

$C=1$ if either of $A$ ``or'' $B$ is $1$

The truth table is as follows:

A	B	C
0	0	0
0	1	1
1	0	1
1	1	1

Truth table for OR gate

Figure 12.2: An OR gate

Eg 2. AND operation is shown in figure 12.3

Figure 12.3: An AND gate

A	B	C
0	0	0
0	1	0
1	0	0
1	1	1

Truth table for AND gate

These were basic gates which are implemented using transistor and other devices.

The transistor implementation is shown if figure 12.4

Figure 12.4: Implementation using a BJT

IC based gates are shown in figure 12.5

Figure 12.5: IC based gates

Other functions

NAND: Not + AND

Figure 12.6: NAND gate

A	B	C
0	0	1
0	1	1
1	0	1
1	1	0

Truth table for NAND gate

NOR gate
Not+OR gate

Figure 12.7: NOR gate

A	B	C
0	0	1
0	1	0
1	0	0
1	1	0

Truth table for NOR gate

X-OR gate
Exclusive-OR gate

Figure 12.8: X-OR gate

A	B	C
0	0	0
0	1	1
1	0	1
1	1	0

Truth table for X-OR gate

X-NOR gate
Exclusive NOR

Figure 12.9: X-NOR gate

A	B	C
0	0	1
0	1	0
1	0	0
1	1	1

Truth table for X-NOR gate.