1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Designing a Digital Circuit

  1. Oct 21, 2014 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    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.
  2. jcsd
  3. Oct 23, 2014 #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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted