Write short notes on- i) De-Morgan's law ii) Latch (NAND and NOR) iii) Astable multivibrator iv) Ring counter

law is a fundamental theorem in Boolean algebra that provides a relationship between the logical operators AND, OR, and NOT. It states that the negation of a conjunction of two propositions is equivalent to the disjunction of their negations, and vice versa. Similarly, the negation of a disjunction of two propositions is equivalent to the conjunction of their negations.

In mathematical notation, De-Morgan's laws can be expressed as follows:

• ¬(A ∧ B) = ¬A ∨ ¬B
• ¬(A ∨ B) = ¬A ∧ ¬B

These laws are widely used in digital circuit design and analysis, as they simplify Boolean expressions and allow for efficient implementation of logic gates.

ii) Latch (NAND and NOR):

A latch is a digital logic circuit that can store one bit of information. It is typically implemented using cross-coupled NAND or NOR gates, forming a feedback loop. The stored bit is determined by the current state of the inputs and the previous state of the latch.

NAND Latch:

A NAND latch is constructed using two NAND gates connected in a cross-coupled configuration. When both inputs (A and B) are at a logical 0, the outputs (Q and ¬Q) are both set to a logical 1. When either input is switched to a logical 1, the corresponding output (Q or ¬Q) is pulled to a logical 0, while the other output remains at a logical 1. This behavior creates a latching effect, where the stored bit remains unchanged until both inputs are simultaneously switched to a logical 0.

NOR Latch:

A NOR latch is constructed using two NOR gates connected in a cross-coupled configuration. The operation of a NOR latch is similar to that of a NAND latch, but with reversed logic. When both inputs (A and B) are at a logical 1, the outputs (Q and ¬Q) are both set to a logical 0. When either input is switched to a logical 0, the corresponding output (Q or ¬Q) is pulled to a logical 1, while the other output remains at a logical 0. Again, this behavior creates a latching effect, where the stored bit remains unchanged until both inputs are simultaneously switched to a logical 1.

iii) Astable Multivibrator:

An astable multivibrator is a free-running oscillator circuit that generates a square wave output without the need for an external trigger. It is typically implemented using two cross-coupled transistors (BJT or MOSFET) and resistors, forming a positive feedback loop.

The operation of an astable multivibrator is based on the charging and discharging of capacitors through resistors. The circuit continuously switches between two unstable states, resulting in a continuous oscillation. The frequency of oscillation is determined by the values of the resistors and capacitors used in the circuit.

iv) Ring Counter:

A ring counter is a sequential logic circuit that consists of a series of flip-flops connected in a closed loop. It is used for counting and storing binary information. The basic principle of a ring counter is that a single pulse is circulated among the flip-flops, causing the stored binary value to shift by one position with each clock pulse.

The operation of a ring counter can be explained as follows:

• Initially, the flip-flops are reset, setting all outputs to 0.
• When a clock pulse is applied, the data in the first flip-flop is shifted to the next flip-flop, and so on.
• The data in the last flip-flop is shifted back to the first flip-flop, completing the cycle.
• This process continues with each clock pulse, causing the binary value stored in the ring counter to shift by one position.

Ring counters are commonly used in applications such as frequency division, modulo counting, and sequence generation.