Everything in the digital world is based on the binary number system. Numerically, this involves only two symbols: 0 and 1. Logically, we can use these symbols or we can equate them with others according to the needs of the moment. Thus, when dealing with digital logic, we can specify that:
- 0 =low = false = no
- 1 = high= true = yes
Using this two-valued logic system, every statement or condition must be either "true" or "false;" it cannot be partly true and partly false. While this approach may seem limited, it actually works quite nicely, and can be expanded to express very complex relationships and interactions among any number of individual conditions.
Representation of logic ‘1’ & ‘0’:
a. Positive logic representation:
If logic ‘1’ represent by higher voltage than logic ‘0’ then its called as positive logic representation.
b. Negative logic representation:
- Logic ‘1’ ------> +5 V and Logic ‘0’ ------> 0 V
- Logic ‘1’ ------> 0 V and Logic ‘0’ ------> -5 V
If logic ‘0’ represent by higher voltage than logic ‘1’ then its called as negative logic representation.
- Logic ‘0’ ------> +5 V and Logic ‘1’ ------> 0 V
- Logic ‘0’ ------> 0 V and Logic ‘1’ ------> -5 V
The table contain all possible combination of inputs and corresponding outputs called as truth table.
The flow of digital signals is controlled by transistors in various configurations depending on the logic family. For most purposes we can imagine that the logic gates are composed of ideal switches with just two states: OPEN and CLOSED. The state of a switch is controlled by a digital signal. The switch remains closed so long as a logical 1 (high) signal is applied and switch is open as logical 0 (low) signals is applied. Logic signals interact by means of gates. The three fundamental gates AND, OR, and NOT, are named after the three fundamental operations of logic that they carry out. The AND and OR gates each have two or more inputs and one output.
The output state is determined by the states of the inputs. The function of each gate is defined by a truth table. The logic gates are:
- NOT Gate
- AND Gate
- OR Gate
- Exclusive-OR Gate
- Exclusive-NOR Gate
- NAND Gate
- NOR Gate