#1. design a BCD to 7-Segment decoder
[Hint: Draw the logical circuit with the corresponding truth table which has 4-bit (DCBA) and when output g,f,e,d, c, b, a]
#2 design an up counter with any convenient Logic designs techniques
#3. Design a magnitude Comparator with takes a random numbers A and B as an input and generates a result as A<B,A>B or A = B.
#4. Draws the block diagram & logical circuit diagrams a Long With their general truth table for the following "flip felpe
#1. Design a BCD to 7-Segment Decoder:
To design a BCD to 7-Segment Decoder, follow these steps:
Step 1: Identify the 7-segment display outputs:
The 7-segment display has 7 segments named a, b, c, d, e, f, and g. Each segment represents a specific character or number display.
Step 2: Construct the truth table:
Create a truth table that maps the BCD input (DCBA) to the corresponding segments (abcdefg) for each digit from 0 to 9.
DCBA | abcdefg
----------------
0000 | 1111110
0001 | 0110000
0010 | 1101101
0011 | 1111001
0100 | 0110011
0101 | 1011011
0110 | 1011111
0111 | 1110000
1000 | 1111111
1001 | 1111011
Step 3: Simplify the logic equations:
From the truth table, simplify the logic equations for each segment (a-g) using Karnaugh maps or boolean algebra.
Step 4: Implement the circuit:
Construct the logical circuit using gates (AND, OR, NOT) based on the simplified logic equations for each segment.
Step 5: Connect the inputs and outputs:
Connect the BCD inputs (DCBA) to the circuit inputs and the segment outputs (abcdefg) to the 7-segment display.
#2. Design an Up Counter:
To design an Up Counter, you can use various techniques such as using D flip-flops or JK flip-flops. Here's a basic design using D flip-flops:
Step 1: Determine the number of bits your counter needs. Let's assume a 4-bit counter.
Step 2: Use D flip-flops to build the counter.
- Connect the D input of the first flip-flop to a clock input signal.
- Connect the output Q of the first flip-flop to the D input of the second flip-flop.
- Repeat this connection for each subsequent flip-flop.
Step 3: Connect the clock input of each flip-flop to a common clock signal.
Step 4: Connect the Q outputs of the flip-flops to the corresponding LED display or any other output mechanism you desire.
Step 5: Connect the Reset input of the first flip-flop to a reset signal, if required. This will reset the counter to zero.
This design will create a simple up counter that increments by one on each clock cycle.
#3. Design a Magnitude Comparator:
To design a Magnitude Comparator, follow these steps:
Step 1: Identify the number of bits for the inputs A and B. Let's assume they are both 4-bit numbers.
Step 2: Compare each bit of A and B, starting from the most significant bit (MSB) to the least significant bit (LSB).
Step 3: Use exclusive OR (XOR) gates to compare the bits. If the corresponding bits of A and B are the same, the XOR output will be 0. If they are different, the XOR output will be 1.
Step 4: Connect the outputs of the XOR gates to an AND gate for each bit. This will generate a 1 output if all the XOR outputs are 1, indicating that A is greater than B.
Step 5: Connect the outputs of the XOR gates to another AND gate. This will generate a 1 output if any of the XOR outputs are 1, indicating that A is less than B.
Step 6: Connect all the AND gate outputs to a decoder circuit to generate the result of A = B, A > B, or A < B.
#4. Draw the Block Diagram & Logical Circuit Diagram for "Flip Flop":
A flip-flop is a sequential circuit element that stores binary data. It can be classified into different types such as D flip-flop, JK flip-flop, SR flip-flop, and T flip-flop. Here, we will draw the block diagram and logical circuit diagram for a D flip-flop.
Block Diagram:
A D flip-flop consists of a D input, a clock input, a Q output, and a Q' (complementary Q) output. The D input represents the data to be stored, the clock input controls when the data is stored, the Q output represents the stored data, and the Q' output is the complement of the Q output.
```
______
| |
D ----| D |-- Q
|flip- |
CLK ---| flop |
| |
|______|
|
Q'
```
Logical Circuit Diagram:
A D flip-flop can be implemented using gates. Here's the logical circuit diagram for a D flip-flop:
```
D ___
----|_ _|
Q |
____ |
-| \|
CLK --| \--- Q
-|___, /
|___|
```
Truth Table:
The truth table for a D flip-flop is as follows:
```
CLK | D | Q(t) | Q(t+1)
----------------------
0 | x | Q | Q
1 | 0 | Q | 0
1 | 1 | Q | 1
```
In the truth table, "Q(t)" represents the current state of the flip-flop, and "Q(t+1)" represents the next state after the clock transitions from 0 to 1. The D input copies its value to the Q output when the clock is high (1).
#1. BCD to 7-Segment Decoder:
Logical Circuit Design:
- Use 4 input lines (DCBA) representing the BCD input.
- Use 7 output lines (g, f, e, d, c, b, a) representing the segments of the 7-segment display.
- Design the logical circuit as follows:
- Set g = ~(D + B + C)
- Set f = ~(~B + ~C + A + ~D)
- Set e = ~(~B + ~C + D)
- Set d = ~(D + ~B + ~C)
- Set c = ~(~C + D)
- Set b = ~(B + ~C + ~D)
- Set a = ~(A + ~D)
Truth Table:
_____________________________________________________
| D | C | B | A | g | f | e | d | c | b | a |
|________|_________|_________|_________|___|___|___|___|___|___|___|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
|________|_________|_________|_________|___|___|___|___|___|___|___|
#2. Up Counter:
Logical Circuit Design:
- Use flip-flops (e.g., D flip-flops) to store the count.
- Use combinational logic gates to generate the next count based on the current count.
- Connect the output of each flip-flop to the input of the next flip-flop in a cascade configuration.
Truth Table:
________________________
| Q2 | Q1 | Q0 |
|_________|________|________|
| 0 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| 1 | 1 | 1 |
|_________|________|________|
#3. Magnitude Comparator:
Logical Circuit Design:
- Use logic gates (e.g., AND, OR, XOR) to compare each bit of numbers A and B.
- Determine if A < B, A > B, or A = B based on the comparison of each bit.
Truth Table:
_________________________________________
| A | B | A < B | A > B | A = B |
|_______|_______|_________|_________|_______|
| 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
|_______|_______|_________|_________|_______|
#4. Flip Flop:
Block Diagram:
-----------------------------------------
| _______ ___________ _______ |
| | | | | | | |
|-->| |->| |->| |-->|
| | | | | | | |
|-->| |->| |->| |-->|
| |_______| |___________| |_______| |
-----------------------------------------
Logical Circuit Diagram:
____________________
| _______ |
| Qn | | |
|----->| D | |
| |_______| |
| |
| Qn+1 _______ |
|------> | ||
| | C ||
| |_______||
--------------------
General Truth Table:
______________________
| C | D | Qn+1 | Qn |
|_____|_____|______|____|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | - | - |
|_____|_____|______|____|
#1. Designing a BCD to 7-Segment Decoder
To design a BCD to 7-Segment Decoder, follow these steps:
1. Start by drawing a logical circuit diagram. In this case, the circuit will have 4 inputs (DCBA) corresponding to the BCD (Binary Coded Decimal) input and 7 outputs (g,f,e,d,c,b,a) corresponding to the segments of a 7-segment display.
2. Assign a truth table for the decoder, where the inputs (DCBA) represent the BCD digit and the outputs (g,f,e,d,c,b,a) represent the segment display.
3. Fill in the truth table based on the relationship between the BCD inputs and the corresponding segment outputs. For example, if DCBA = 0000, then g=1, f=1, e=1, d=1, c=1, b=1, a=0 would correspond to the digit '0'.
4. Based on the truth table, implement the logic circuit using logic gates (AND, OR, NOT) and any other necessary combinational logic elements.
5. Ensure that the logic circuit is correct by testing it with different BCD inputs and verifying that the corresponding segment outputs match the expected results.
Remember to label the inputs and outputs on the circuit diagram and provide appropriate gate or logic element symbols for clarity.
#2. Designing an Up Counter
To design an up counter, there are various convenient logic design techniques. One common method is using D flip-flops.
Here's one way to design an up counter using D flip-flops:
1. Determine the number of bits you want for your counter. Let's say we want a 4-bit counter.
2. Design a clock signal that will trigger the counter to increment. You can use a clock signal generator such as an oscillator.
3. Connect the D input of each flip-flop to the output of the previous flip-flop. For example, connect D1 to Q0, D2 to Q1, D3 to Q2, and D4 to Q3.
4. Connect the clock signal to the clock input of all the flip-flops.
5. Connect the inverted output (Q̅) of each flip-flop to the clear or reset input of the next flip-flop. This ensures that the counter resets to zero when it reaches the maximum count.
6. Ensure that the output of each flip-flop (Q0-Q3) is connected to LEDs or any other output display device to visualize the count.
This design will result in an up counter that increments by 1 with each clock pulse, starting from 0000 and going up to the maximum count based on the number of bits used (e.g., 1111 for a 4-bit counter).
#3. Designing a Magnitude Comparator
To design a magnitude comparator, follow these steps:
1. Determine the number of bits you want for your comparator. Let's say we want a 4-bit comparator.
2. Design input circuits for two random input numbers, A and B, with 4 bits each.
3. Implement the logic for greater than (A>B), less than (A<B), and equal to (A=B) comparisons. This can be done using combinational logic elements such as AND, OR, and XOR gates.
4. Connect the output of each comparison (A>B, A<B, A=B) to appropriate output indicators (e.g., LEDs or display devices) to represent the result.
5. Test the comparator with different random numbers A and B to verify that the comparison outputs are correct.
Ensure that the input circuits are labeled with A and B, and the comparison outputs are clearly labeled with A>B, A<B, and A=B for clarity.
#4. Designing a Flip-Flop
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