The Question

Use two 74LS163, one 74LS74A, XNOR gates and AND gate(s) to build a circit that can "add" two given "4-bit binary numbers" A and B.

Here is how the circuit computes SUM = A+B (for SUM <= 1111):

  1. Load A into a counter.

  2. Count up by number of clocks given by B to obtain SUM.

Hint: one 74LS163 will give you the SUM. The other 74LS163 will tell the first one when to stop counting.

You must place A and B into the inputs of the circuit, and initialise the circuit by setting/resetting/loading necessary register(s) using a signal INITIALISE = 0.





What I've come up with so far

I am very new to this topic so I'm not sure if any of this is correct.

Here is a simple chart of how I believe the circuit works: chart of how I believe the circuit works

State diagram for SUM: State diagram for SUM

State diagram for B: State diagram for B

I don't know how to continue next. Could anyone please help? Thank you!

  • 1
    \$\begingroup\$ Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also here. \$\endgroup\$
    – Dave Tweed
    Commented Nov 14, 2019 at 14:32
  • \$\begingroup\$ Hi! I'm sorry that I have so little to contribute cause I'm really new to this topic. I think I can start by drawing two state diagrams: 1) A as states and E (whether the circuit needs to keep counting) as the input; 2) B as states and E as the input. Am I on the right track? \$\endgroup\$
    – Vero
    Commented Nov 15, 2019 at 13:36

1 Answer 1


The hint is important. You'll have two counters. One gets loaded with "A". What do you load into the other one so that it can tell you when you've incremented the first counter by the right number of cycles?

They're trying to get you to think in terms of state machines. This one is a bit complicated, because there are three state machines involved — the two counters, plus some sort of sequencer that controls the overall operation. Draw yourself some state diagrams that show what needs to happen and in what order.


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