#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
i) S-R-Flip Flop
ii) D. Flip Flop
III) J-k-Flip Flop
IV) T-Flip Flop
#1. Designing a BCD to 7-Segment Decoder:
A BCD to 7-Segment Decoder is used to convert Binary Coded Decimal (BCD) inputs to the respective outputs for a 7-segment display. Here's a step-by-step process to design a BCD to 7-segment decoder:
Step 1: Identify the inputs and outputs:
- Inputs: 4-bit BCD inputs (D, C, B, A)
- Outputs: 7-segment display outputs (g, f, e, d, c, b, a)
Step 2: Create a truth table:
The truth table will have 4 inputs (D, C, B, A) and 7 outputs (g, f, e, d, c, b, a). Each output represents a specific segment of the 7-segment display.
D | C | B | A || g | f | e | d | c | b | a |
--------------------------------
0 | 0 | 0 | 0 || 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 0 | 1 || 0 | 1 | 1 | 0 | 0 | 0 | 0 |
(continue the truth table for all possible combinations of D, C, B, A)
Step 3: Simplify Boolean expressions for each output:
Using Karnaugh Maps or any other simplification technique, derive Boolean expressions for each output (g, f, e, d, c, b, a) based on the truth table.
Step 4: Create a logical circuit diagram:
With the simplified Boolean expressions, design a logical circuit diagram that represents the BCD to 7-segment decoder. The logical circuit will consist of logic gates like AND, OR, and NOT gates.
Step 5: Implement the circuit:
Based on the logical circuit diagram, you can use either discrete logic gates or a programmable logic device (PLD) to implement the BCD to 7-segment decoder circuit.
Note: The final step-by-step details of the logical circuit diagram may depend on the simplification technique used and specific requirements.
#1. BCD to 7-Segment Decoder:
A BCD to 7-segment decoder is a combinational logic circuit that converts a 4-bit binary-coded decimal (BCD) input into the corresponding 7-segment display output. The 7-segment display has 7 individual LEDs denoted as a, b, c, d, e, f, and g.
Logical Circuit Diagram:
The logical circuit diagram for the BCD to 7-segment decoder is as follows:
```
_________ _________ _________ _________
| | | | | | | |
--| a |--| b |--| c |--| d |--
|_________| |_________| |_________| |_________|
_________ _________ _________ _________
| | | | | | | |
--| e |--| f |--| g |--| g |--
|_________| |_________| |_________| |_________|
```
Truth Table:
The truth table for the BCD to 7-segment decoder is as follows:
```
DCBA | a b c d e f g
_________|_____________________________
0000 | 1 1 1 1 1 1 0
0001 | 0 1 1 0 0 0 0
0010 | 1 1 0 1 1 0 1
0011 | 1 1 1 1 0 0 1
0100 | 0 1 1 0 0 1 1
0101 | 1 0 1 1 0 1 1
0110 | 1 0 1 1 1 1 1
0111 | 1 1 1 0 0 0 0
1000 | 1 1 1 1 1 1 1
1001 | 1 1 1 0 0 1 1
... | ... (continued for all BCD inputs)
```
#2. Up Counter:
An up counter is a sequential logic circuit that counts upwards from a specified starting value. It is commonly used in digital circuits to generate sequences, clock divisions, etc.
One convenient logic design technique for designing an up counter is by using D flip-flops and cascading them.
Logical Circuit Diagram:
The logical circuit diagram for an up counter with D flip-flops can be represented as follows:
```
_______ _______
D0 ----| |----- Q0 ----| |----- Q0
--| D FF | | D FF |
CLK |_______| |_______|
.
.
_______ _______ .
| |----- Q1 ----| |
| D FF | | D FF |
|_______| |_______|
.
.
.
_______ _______ .
| |----- Q2 ----| |
| D FF | | D FF |
|_______| |_______|
.
.
.
_______ _______
| |----- Q3 ----| |
| D FF | | D FF |
|_______| |_______|
```
Truth Table:
The truth table for each D flip-flop in the up counter is as follows:
```
CLK | D | Q
_________|_________|_________
0 | X | Q(t-1)
1 | X | D(t-1)
```
#3. Magnitude Comparator:
A magnitude comparator is a combinational logic circuit that compares two numbers and determines their relationship - whether one number is less than (<), greater than (>), or equal to (=) the other number.
Logical Circuit Diagram:
The logical circuit diagram for a magnitude comparator can be represented using logic gates such as AND, OR, and XOR gates.
```
--------
A ----| | _______
B ----| |---> A>B --| |
| MAG | | |
| COMP. |---> A=B --| |
| | | |---> A<B
-------- |_______|
```
Truth Table:
The truth table for the magnitude comparator is as follows:
```
A | B | A>B | A=B | A<B
________|________|_________|_________|_______
0 | 0 | 0 | 1 | 0
0 | 1 | 0 | 0 | 1
1 | 0 | 1 | 0 | 0
1 | 1 | 0 | 1 | 0
```
#4. Flip Flops:
A flip-flop is a sequential logic circuit that stores a single bit of data, allowing it to remember its state indefinitely until a new input is received.
i) S-R Flip Flop:
Logical Circuit Diagram:
The logical circuit diagram for an S-R flip-flop is as follows:
```
______
S ---| |
| S-R |---- Q
R ---| Flip |
| Flo |
G ---| op |---- Q'
______
```
Truth Table:
The truth table for an S-R flip-flop is as follows:
```
S | R | Q | Q'
________|_______|_______|_______
0 | 0 | Q | Q
0 | 1 | 0 | 1
1 | 0 | 1 | 0
1 | 1 | X | X
```
ii) D Flip Flop:
Logical Circuit Diagram:
The logical circuit diagram for a D flip-flop is as follows:
```
______
D ---| |
| D |---- Q
| Flip |
G ---| Flo |
| op |---- Q'
|______|
```
Truth Table:
The truth table for a D flip-flop is as follows:
```
D | Q | Q'
________|_______|_______
0 | 0 | 1
0 | 1 | 0
1 | 1 | 0
1 | 0 | 1
```
iii) J-K Flip Flop:
Logical Circuit Diagram:
The logical circuit diagram for a J-K flip-flop is as follows:
```
______
J ---| |
| J-K |---- Q
K ---| Flip |
| Flo |
G ---| op |---- Q'
|______|
```
Truth Table:
The truth table for a J-K flip-flop is as follows:
```
J | K | Q | Q'
________|_______|_______|_______
0 | 0 | Q | Q
0 | 1 | 0 | 1
1 | 0 | 1 | 0
1 | 1 | Q' | Q
```
iv) T Flip Flop:
Logical Circuit Diagram:
The logical circuit diagram for a T flip-flop is as follows:
```
______
T ---| |
| T |---- Q
| Flip |
G ---| Flo |
| op |---- Q'
|______|
```
Truth Table:
The truth table for a T flip-flop is as follows:
```
T | Q | Q'
________|_______|_______
0 | Q | Q
1 | 1 | 0
```
#1. Designing a BCD to 7-Segment Decoder:
A BCD to 7-Segment Decoder is a logic circuit that takes a 4-bit Binary Coded Decimal (BCD) input and converts it into the corresponding pattern of outputs to drive a 7-segment display. Here's how you can approach designing this decoder:
1. Start by listing out the BCD values and their corresponding 7-segment display outputs:
BCD (DCBA) | 7-Segment (gfedcba)
-------------------------------
0000 | 1111110
0001 | 0110000
0010 | 1101101
0011 | 1111001
... (continue for all BCD values)
2. Identify the logic needed to generate each segment (a, b, c, d, e, f, g) based on the BCD input bits. For example, to generate the 'a' segment output, you need to consider which BCD values should light up the 'a' segment.
3. Create a truth table that lists the BCD inputs and the corresponding outputs for each segment.
4. Apply Boolean logic to determine the logic expression for each segment output. This can be done using Karnaugh maps or Boolean algebra techniques.
5. Create a logic circuit diagram by combining the logic expressions for each segment output.
6. Test the circuit using a simulator or by building it on a breadboard.
#2. Designing an Up Counter:
To design an Up Counter, you can use various logic design techniques, such as using flip-flops, combinational logic circuits, or dedicated counter chips. Here's one simple approach using D flip-flops:
1. Determine the number of bits required for your counter based on the desired count range.
2. For each bit, use a D flip-flop connected in a cascade arrangement. Connect the output of each flip-flop to the D input of the next flip-flop.
3. Connect the clock input of the first flip-flop to the clock signal that will increment the counter.
4. Connect any necessary control circuitry or additional logic to implement reset or enable functionality, if desired.
5. The output of each flip-flop represents a bit in the binary counter.
6. The most significant bit (MSB) can be used to trigger additional logic or generate an overflow signal when the counter reaches its maximum value.
7. Test the counter by providing clock pulses and observing the count on the output bits.
#3. Designing a Magnitude Comparator:
To design a Magnitude Comparator, you can use a combination of logic gates to compare two numbers (A and B) and generate the result as A<B, A>B, or A=B. Here's an approach:
1. Begin by comparing the most significant bits (MSBs) of A and B. Use an XOR gate to compare them.
2. If the MSBs of A and B are equal, move to the next lower significant bit and repeat the comparison process.
3. If the MSBs of A and B are not equal, the result is determined. If A is greater than B, set A>B output. If A is less than B, set A<B output.
4. If you reach the least significant bit (LSB) and all previous bits were equal, set A=B output.
5. Implement the necessary logic expressions using gates and connections to derive the outputs for A<B, A>B, and A=B.
6. Test the comparator using different sets of random input numbers to ensure the desired outputs are generated.
#4. Designing Various Flip-Flops:
i) S-R Flip Flop:
- The S-R (Set-Reset) Flip Flop has two inputs: S (Set) and R (Reset).
- Draw a block diagram that represents the S-R Flip Flop with an S-R latch and feedback connections.
- The truth table for an S-R Flip Flop is as follows:
S | R | Q | Q'
------------------
0 | 0 | Q(t) | Q'(t)
0 | 1 | 0 | 0
1 | 0 | 1 | 1
1 | 1 | Invalid (results in indeterminate state)
ii) D Flip Flop:
- The D Flip Flop has one input: D (Data).
- Draw a block diagram that represents the D Flip Flop with a D latch and feedback connections.
- The truth table for a D Flip Flop is as follows:
D | Q | Q'
------------------
0 | Q(t) | 0
1 | Q(t) | 1
iii) J-K Flip Flop:
- The J-K Flip Flop has two inputs: J and K.
- Draw a block diagram that represents the J-K Flip Flop with a J-K latch and feedback connections.
- The truth table for a J-K Flip Flop is as follows (assuming positive-edge triggered):
J | K | Q(t) | Q'(t+1)
---------------------
0 | 0 | Q(t) | Q'(t)
0 | 1 | 0 | 1
1 | 0 | 1 | 0
1 | 1 | Q(t) | ~Q(t)
iv) T Flip Flop:
- The T Flip Flop has one input: T (Toggle).
- Draw a block diagram that represents the T Flip Flop with a T latch and feedback connections.
- The truth table for a T Flip Flop is as follows:
T | Q(t) | Q'(t+1)
----------------
0 | Q(t) | Q'(t)
1 | ~Q(t) | ~Q(t)
Note: The symbols used in the diagrams for each flip flop may vary, so it's important to refer to the design conventions or standards used in your specific context.