Question

Implement a 3-bit counter that counts in two different orders. Your circuit should have a Button named CLK, a Button named RESET, and an input pin named Gray (for Gray code). It should have 3 LED displays, named L0, L1, and L2. The first thing the Test option does it ensure you have the correct inputs and outputs. The inputs and outputs are identical to those for the previous 3-bit counter except for the addition of the extra pin named Gray. The names are case sensitive.

When G is false, the counter is an up counter, counting in steps of 1. Each clock pulse increases the count by one: 0, 1, 2, 3, 4, 5, 6, 7, 0, etc.
When G is true, the counter is a gray code counter counting in gray code order: 0, 1, 3, 2, 6, 7, 5, 4, then back to 0. In binary, that is (000, 001, 011, 010, 110, 111, 101, 100, then back to 000).

Example: Suppose the current output is 101. If G=1, the value after the next clock will be the next value in the gray code sequence, 100. If G=0, the value after the next clock will be the next value sequentially, 110.

Draw the Karnaugh map and truth table and complete the circuit diagram using D flip-flop SR

Answer 1

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Step-by-step explanation:

Answer 2

To implement a 3-bit counter that counts in two different orders using D flip-flops and considering the Gray code functionality, I'll provide a concise representation of the Karnaugh map, truth table, and a basic circuit diagram.

Karnaugh Map for Gray Code Counter:

Current State (Q2Q1Q0) Next State (Q2+ Q1+ Q0+)

000 001

001 011

011 010

010 110

110 111

111 101

101 100

100 000

Truth Table:

G Current State (Q2Q1Q0) Next State (Q2+ Q1+ Q0+)

0 000 001

0 001 010

0 010 011

0 011 100

0 100 101

0 101 110

0 110 111

0 111 000

1 000 001

1 001 011

1 011 010

1 010 110

1 110 111

1 111 101

1 101 100

1 100 000

Circuit Diagram Using D Flip-Flop (SR):

_____ _____ _____

G ----|D Q|-------|D Q|-------|D Q|----

| | | | | |

CLK --|>CLK Q|-----> |>CLK Q|---->|>CLK Q|---

|_____| |_____| |_____|

| | |

| _______ | _______ |

RESET --|->|D Q|-> |->|D Q|-> |--> and so on...

|__| | |__| |

| | | |

Gray ------|------|------|------|-----------

This circuit diagram represents a 3-bit counter with D flip-flops, CLK (Clock) and RESET buttons, and an additional input pin named Gray for controlling the counting sequence. The flip-flops are arranged to change states based on the Clock signal and the Gray code input, following the truth table provided above.