Digital Logic Midterm

Explain the behavior of an encoder. What are its inputs and outputs?

An encoder is a digital circuit that converts a set of binary inputs into a unique binary code. The binary code represents the position of the input and is used to identify the specific input that it active. (The opposite of a decoder) It has a maximum of 2^n input lines and ‘n’ output lines, hence it encodes the information from 2^n inputs into an n-bit code.

• A 4 to 2 encoder has 4 (2²) inputs and 2 (n=2) outputs

• A 8 to 3 encoder has 8 (2³) inputs and 3 (n=3) outputs

Explain the behavior of a decoder. What are its inputs and outputs?

A decoder is used to convert binary-coded inputs into a unique set of outputs. (The opposite of an encoder) A decoder takes n inputs and has 2^n outputs. It is mainly used to convert binary coded data into multiple outputs.

• 2 bit decoder has 2 inputs and 4 outputs (2² = 4)

• 4 bit decoder has 4 inputs and 16 outputs (2^4 = 16)

What is an S-Latch?

• Set-Reset Latch

• Two inputs: S (Set) and R (Reset)

• The S input sets the output to 1

• The R input resets the input to 0

• When both S and R are at 1, the latch is said to be in an “undefined” state

S | R | Q | Q’

————————--

0 | 0 | latch | latch hold (no change)

0 | 1 | 0 | 1 Reset

1 | 0 | 1 | 0 Set

1 | 1 | 0 | 0 Invalid

What is a flip flop?

A circuit that maintains a state until directed by input to change the state. A flip-flop is a component that is used to store one single bit of information.

JK Flip Flop

• Input Set (J) and Reset (K)

J | K | Q | Q+

0 | x | 0 | 0

1 | x | 0 | 1

x | 0 | 1 | 1

x | 1 | 1 | 0

1. J = 0, K = 0 (No Change): Here, the output Q(n+1) stays the same. This means the next state (Q(n+1)) is just like the current one (Qn).

2. J = 0, K = 1 (Reset State): In this case, the next state is reset to 0 (Q(n+1) = 0), no matter what the current state is (Qn).

3. J = 1, K = 0 (Set State): Now, the next state gets set to 1 (Q(n+1) = 1), again, no matter what’s happening in the current state (Qn).

4. J = 1, K = 1 (Toggle State): In this state, the output Q(n+1) toggles. So if the current state is set (Qn = 1), it will change to 0 (Q(n+1) = 0). If it’s reset (Qn = 0), then it flips to 1 (Q(n+1) = 1).

T Flip Flop

• Toggle Flip Flop

• It’s able to toggle its output depending upon the input

• Toggle indicates that the bit will be flipped (0 to 1 or 1 to 0)

T | Q | Q+

0 | 0 | 0

1 | 0 | 1

0 | 1 | 1

1 | 1 | 0

D Flip Flop

• Delay flip flop or data flip flop

• When clock input is high, the data is transferred to the output of the flip flop.

• When the clock input is low, the output of the flip flop is held in its previous state.

D | Q | Q+

0 | 0 | 0 

1 | 0 | 1 

0 | 1 | 0

1 | 1 | 1 

Q+ = D

What is the purpose of the clock signal?

• Serves as a metronome for digital circuits

• ensures that all components operate in sync

What is the difference between an asynchronous and synchronous component?

• Synchronous communication requires the sender to wait for an immediate response, making it suitable for real-time interactions.

• Synchronous = clock

• Asynchronous communication, on the other hand, allows the sender to proceed without waiting, enabling better scalability and flexibility in distributed systems.

Multiplexers

Equation for a 2×1 multiplexer: Y = (D0 S’) + (D1 S)