Basic Logic Operations

There are 5 basic logic operations representing the
digital electronic circuits.

NOT

AND

OR

NAND

NOR

The device/circuit that performs single logic
operation is called Gate.

Combinational Gates

The gates that perform one or more of the basic
logical operations are referred to as Combinational Gates. Outputs depend only
on the present value of the inputs.

Sequential Gates

The gates that perform sequential logic operations
are referred to as Sequential Gates. Outputs depend on the past values of the
inputs as well as present values. For all digital circuits, a variable can only
have two states, 0 and 1. Such variable is called Binary variable. Considering
voltage as a variable, Binary 0 state representing low voltage and binary 1
state representing high voltage.

Digital Logic Circuits -Inverter

If the input voltage is low, the output voltage will
be high and vice versa. Since this device performs logical NOT operation, this
device is also called NOT gate. It makes no difference if the inverting circle
is at the input or output. Non-Inverting devices are also termed as Buffers. Buffers
are used to regenerate voltage levels. Buffers adjust degraded high levels to
higher and degraded low levels to lower.

Ideal Logic – Inverter

A typical operating voltage of many logic families
is 5V.Ideal Power dissipation of all logic families is zero. In actual case,
the power dissipation is minimized for optimum design. Ideally, the logical 1
output voltage is at the power supply voltage Vcc. Ideally, the logical 0 output
voltage is at ground (0V).

Ideal Logic – Static & Power Characteristic

Ideally, the transition between output logic states
occurs abruptly at an input of Vcc/2. Logical input 0 is represented by the
voltage range 0 ≤ VIN <
Vcc/2.Logical input 1 is represented by the voltage range Vcc/2 < VIN <
Vcc. VIN =Vcc/2 has an undefined output and gives unpredictable results.

Ideal Logic – Transient Characteristic

Upon transition of the input from logical 0 to
logical 1, the output instantaneously switches from logical 1 to logical 0
without any delay.

In actual case, the transition between states is not
instantaneous and a delay between the output and input transitions is present.

Ideal Logic – Input & Output Impedances

Transient response and driving ability (fan-out) of
logic gates are directly dependent upon the gate’s input and output impedance.

gate’s input and output impedance. Ideal Logic –
Input & Output Impedances

The previous figure shows a logic inverter driving
multiple (identical) logic inverters. It is observed that the driving gate must
provide enough output current to drive all the load gates. IOUT = NI’IN where
the primed terms referred to load gates.

The input current is zero for a very large input
impedance and driving capabilities are maximized. An infinite input impedance
is desired to obtain infinite driving capability.

The input capacitance of load gates must be charged
through the output resistance of the driving inverter. Thus, a smaller output
resistance will provide a larger charging current for the load capacitance and
a faster switching time. Ideally, the output resistance must be zero.

A smaller input capacitance can also speed up the
switching time of the load gates.

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