A) Implement a full adder circuit with a (3 to 8) line decoder and two OR gates. b) Why Analog to Digital converters is needed? Explain any one Digital converters.

a) Implement a full adder circuit with a (3 to 8) line decoder and two OR gates.

A full adder is a digital circuit that performs addition of two one-bit numbers with a carry input. The full adder produces a sum output and a carry output. The truth table for a full adder is as follows:

A (Input)	B (Input)	Cin (Carry In)	Sum (Output)	Cout (Carry Out)
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

To implement a full adder using a (3 to 8) line decoder and two OR gates, we can map the truth table of the full adder to the outputs of the decoder. A (3 to 8) line decoder has 3 input lines and 8 output lines. It activates one of the eight outputs depending on the binary value of the three inputs.

Here are the steps to implement the full adder:

1. Label the inputs of the decoder as A, B, and Cin.
2. Connect the outputs of the decoder to the OR gates in such a way that the Sum and Cout can be obtained according to the truth table.

Let's denote the outputs of the decoder as D0, D1, ..., D7, where each output corresponds to a combination of the inputs A, B, and Cin. For example, D0 is active when A=0, B=0, and Cin=0, and D7 is active when A=1, B=1, and Cin=1.

The Sum output can be obtained by OR'ing the outputs of the decoder that correspond to the cases where the Sum is 1 (D1, D2, D4, D7). The Cout output can be obtained by OR'ing the outputs of the decoder that correspond to the cases where Cout is 1 (D3, D5, D6, D7).

Here's the mapping:

Decoder Output	Sum (1)	Cout (1)
D0	0	0
D1	1	0
D2	1	0
D3	0	1
D4	1	0
D5	0	1
D6	0	1
D7	1	1

Now, connect the decoder outputs to the OR gates as follows:

• Sum = D1 OR D2 OR D4 OR D7
• Cout = D3 OR D5 OR D6 OR D7

Using the above mapping, we can construct the full adder circuit with the decoder and OR gates.

b) Why Analog to Digital converters are needed? Explain any one Digital converter.

Analog to Digital Converters (ADCs) are needed for several reasons:

1. Digital Processing: Most modern electronic devices process information digitally. To use analog signals (like sound, temperature, etc.) with digital systems, we need to convert them into digital form.
2. Storage and Transmission: Digital data is easier to store and transmit without degradation compared to analog data.
3. Compatibility: Digital signals are compatible with digital systems like computers, smartphones, and digital communication systems.

Example: Successive Approximation Register (SAR) ADC

The Successive Approximation Register ADC is a popular type of ADC known for its balance between speed and complexity. It works by approximating the analog input voltage through a binary search algorithm.

Here's how a SAR ADC works:

1. Initialization: The SAR ADC initializes the Successive Approximation Register (SAR) to the midpoint value (for an n-bit ADC, this would be 2^(n-1)).
2. Comparison: The SAR value is converted to an analog voltage using a Digital to Analog Converter (DAC) and compared with the input voltage using a comparator.
3. Adjustment: Depending on the comparator's output, the SAR adjusts the next bit to a 1 or 0 and repeats the comparison.
4. Iteration: This process is repeated for each bit in the SAR until all bits have been set.
5. Result: The final SAR value is the digital representation of the analog input voltage.

The SAR ADC is efficient and suitable for medium to high-resolution applications, such as data acquisition systems and digital oscilloscopes.