Optimizing Digital Circuit Design with Radix Four Addition

In summary, the conversation discusses different solutions for a problem involving multiplexors. One solution involves using 10 4:1 gates, while another solution uses only four 4:1 and four 2:1 gates by using a radix four system to determine if a number is divisible by 3. This method involves adding bits in groups of two and using a carry to optimize the calculation, ultimately using only 6 gates.
  • #1
Vishera
72
1

Homework Statement



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Homework Equations

The Attempt at a Solution


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Is there any more efficient way to solve this problem? The resultant functions are quite complicated and I was wondering if there is any way to make them simpler so it would be easier to draw the circuit.
 
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  • #2
If you're using 2:1 and 4:1 multiplexors, your solution yields 10 of the 4:1 gates.

I have a solution that uses four 4:1 and four 2:1 - but it's a bit complicated. In the same way that you can tell whether a number is divisible by 9 by adding up the decimal digits, you can tell is a number is divisible by 3 by adding up the radix four digits. Radix four is binary in groups of 2 bits. So, if A=x1x2 and B=x3x4, the C=A+B (addition, not oring) would give you the total sum of the base 4 digits. But for optimization you don't completely calculate C. With 2 gate (one 4:1 and one 2:1) you can add two bits and generate a carry. So you add D=x1+x3, E=x2+x4, F=D+E and you've used 6 gates.

If you want, you should be able to figure it from there.
 

1. What is a digital circuit?

A digital circuit is an electronic circuit that works with discrete signals or binary values of 0 and 1, known as digital signals, to perform logic operations and process information. It is the foundation of digital electronics and is used in various electronic devices such as computers, smartphones, and calculators.

2. What are the basic components of a digital circuit?

The basic components of a digital circuit include logic gates, flip-flops, registers, counters, and multiplexers. These components are interconnected to perform specific logic operations and create a functional circuit.

3. How do you design a digital circuit?

The design process of a digital circuit involves several steps such as defining the logic operations, selecting the appropriate components, creating a schematic diagram, simulating the circuit, and testing its functionality. It also requires knowledge of digital logic and circuit analysis techniques.

4. What factors should be considered while designing a digital circuit?

There are several factors that should be considered while designing a digital circuit, including the speed and accuracy of the circuit, power consumption, size and complexity, and cost. These factors can impact the performance and functionality of the circuit and should be carefully evaluated during the design process.

5. What are the different types of digital circuits?

There are three main types of digital circuits: combinational circuits, sequential circuits, and arithmetic circuits. Combinational circuits perform logic operations on inputs to produce an output, sequential circuits use memory elements to store information and produce outputs based on current and previous inputs, and arithmetic circuits perform arithmetic operations on binary numbers.

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