# Synchronous 3-bit up/down counter

• Hurly
In summary, the task is to design and implement a synchronous 3-bit up/down counter with a specific decimal code sequence. The counter should count "up" when an UP/DOWN control input is 1 and "down" when the control input is 0. The decimal and binary sequences for counting "up" and "down" are provided. The individual is seeking help with the flip-flop transition table and simplified logic expressions for flip-flop inputs and has already built the circuit in logisim but it is not counting to the correct sequence.
Hurly

## Homework Statement

Design and implement a synchronous 3-bit up/down counter with the following decimal code sequence: 0,1,3,5,7,6,4,2,0,… The counter should count “up” when an UP/DOWN control input Y is 1, and count “down” when the control input is 0.

• Counting “up”
decimal: 0,1,3,5,7,6,4,2,0,…
binary: 000,001,011,101,111,110,100,010,000,…
• Counting “down”
decimal: 0,2,4,6,7,5,3,1,0,…
binary: 000,010,100,110,111,101,011,001,000,…

2. The attempt at a solution

I don't know if the state diagram and Table are right but I am having trouble with the flip-flop transition table and the simplified logic expressions for flip-flop inputs. could someone help me out please

imageshack.us/f/822/statediagram2.png/

Picture of state diagrams and state table

imageshack.us/f/822/statediagram2.png/

Picture of state diagrams and state table

Please can anyone help me i have built the circuit in logisim but its not counting to what it was suppose to

its counting 0,4,5,7,6,2,3,0

## What is a synchronous 3-bit up/down counter?

A synchronous 3-bit up/down counter is a digital circuit that can count up or down depending on the input signals. It has three flip-flops (memory elements) that store the current count value and a set of logic gates that control the counting direction and enable the counter to synchronize with a clock signal.

## What is the difference between a synchronous and asynchronous counter?

In a synchronous counter, all flip-flops are triggered by the same clock signal, ensuring that all stages change their state at the same time. In an asynchronous counter, each flip-flop is triggered by the output of the previous stage, resulting in a delay between each stage's state change.

## How does a 3-bit up/down counter count in both directions?

A 3-bit up/down counter has two input signals, "up" and "down", which determine the counting direction. When the "up" signal is high, the counter counts up (increases its value by 1) on each clock pulse. When the "down" signal is high, the counter counts down (decreases its value by 1) on each clock pulse. The inputs are typically controlled by a control unit or a microcontroller.

## What is the maximum count value of a 3-bit up/down counter?

A 3-bit up/down counter can store a maximum count value of 7 (or 111 in binary). This is because it has three flip-flops, each of which can store a binary digit (0 or 1). Therefore, the maximum count value is 2^3 - 1 = 7.

## What are the applications of a synchronous 3-bit up/down counter?

Synchronous 3-bit up/down counters are commonly used in digital systems for various applications, such as controlling electronic devices, keeping track of time or events, implementing sequential logic circuits, and more. They are also used in microcontrollers, calculators, and other electronic devices that require counting functionality.

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