#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. 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 answer