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Computing X^2 with Combinational Logic [Digital Logic Project]
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I've been working on an assignment for my digital logic class in which we are to design a circuit that computes the value of an input (x) and outputs y, where y = x^2, all in binary. I've made a little progress, but computing past the 5th binary digit is stumping me. The restrictions are this: * Inputs for x are x0, x1, x2, x3, x4 (5 digits, binary) * Output for y is y0, y1,...... y9 (10 digits, binary) * x can range from 0 to 31 and consequently, y can range from 0 to 961 ( = 31^2) We are to make a truth table and write switching functions for all y outputs. Here is what I have so far: [B]Truth Table for x[SUB]input[/SUB] and y[SUB]output[/SUB]:[/B] [B]Where y = x^2…[/B] [TABLE="width: 624, align: left"] [TR] [TD][B]x = (x[SUB]4[/SUB], x[SUB]3[/SUB], x[SUB]2[/SUB], x[SUB]1[/SUB], x[SUB]0[/SUB])[/B][/TD] [TD][B]y = (y[SUB]9[/SUB], y[SUB]8[/SUB], y[SUB]7[/SUB], y[SUB]6[/SUB], y[SUB]5[/SUB], y[SUB]4[/SUB], y[SUB]3[/SUB], y[SUB]2[/SUB], y[SUB]1[/SUB], y[SUB]0[/SUB])[/B][/TD] [/TR] [TR] [TD][B]0 0 0 0 0[/B][/TD] [TD]0 0 0 0 0 0 0 0 0 0[/TD] [/TR] [TR] [TD][B]0 0 0 0 1[/B][/TD] [TD]0 0 0 0 0 0 0 0 0 1[/TD] [/TR] [TR] [TD][B]0 0 0 1 0[/B][/TD] [TD]0 0 0 0 0 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]0 0 0 1 1[/B][/TD] [TD]0 0 0 0 0 0 1 0 0 1[/TD] [/TR] [TR] [TD][B]0 0 1 0 0[/B][/TD] [TD]0 0 0 0 0 1 0 0 0 0[/TD] [/TR] [TR] [TD][B]0 0 1 0 1[/B][/TD] [TD]0 0 0 0 0 1 1 0 0 1[/TD] [/TR] [TR] [TD][B]0 0 1 1 0[/B][/TD] [TD]0 0 0 0 1 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]0 0 1 1 1[/B][/TD] [TD]0 0 0 0 1 1 0 0 0 1[/TD] [/TR] [TR] [TD][B]0 1 0 0 0[/B][/TD] [TD]0 0 0 1 0 0 0 0 0 0[/TD] [/TR] [TR] [TD][B]0 1 0 0 1[/B][/TD] [TD]0 0 0 1 0 1 0 0 0 1[/TD] [/TR] [TR] [TD][B]0 1 0 1 0[/B][/TD] [TD]0 0 0 1 1 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]0 1 0 1 1[/B][/TD] [TD]0 0 0 1 1 1 1 0 0 1[/TD] [/TR] [TR] [TD][B]0 1 1 0 0[/B][/TD] [TD]0 0 1 0 0 1 0 0 0 0[/TD] [/TR] [TR] [TD][B]0 1 1 0 1[/B][/TD] [TD]0 0 1 0 1 0 1 0 0 1[/TD] [/TR] [TR] [TD][B]0 1 1 1 0[/B][/TD] [TD]0 0 1 1 0 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]0 1 1 1 1[/B][/TD] [TD]0 0 1 1 1 0 0 0 0 1[/TD] [/TR] [TR] [TD][B]1 0 0 0 0 [/B][/TD] [TD]0 1 0 0 0 0 0 0 0 0[/TD] [/TR] [TR] [TD][B]1 0 0 0 1[/B][/TD] [TD]0 1 0 0 1 0 0 0 0 1[/TD] [/TR] [TR] [TD][B]1 0 0 1 0[/B][/TD] [TD]0 1 0 1 0 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]1 0 0 1 1[/B][/TD] [TD]0 1 0 1 1 0 1 0 0 1[/TD] [/TR] [TR] [TD][B]1 0 1 0 0[/B][/TD] [TD]0 1 1 0 0 1 0 0 0 0[/TD] [/TR] [TR] [TD][B]1 0 1 0 1[/B][/TD] [TD]0 1 1 0 1 1 1 0 0 1[/TD] [/TR] [TR] [TD][B]1 0 1 1 0[/B][/TD] [TD]0 1 1 1 1 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]1 0 1 1 1[/B][/TD] [TD]1 0 0 0 0 1 0 0 0 1[/TD] [/TR] [TR] [TD][B]1 1 0 0 0[/B][/TD] [TD]1 0 0 1 0 0 0 0 0 0[/TD] [/TR] [TR] [TD][B]1 1 0 0 1[/B][/TD] [TD]1 0 0 1 1 1 0 0 0 1[/TD] [/TR] [TR] [TD][B]1 1 0 1 0[/B][/TD] [TD]1 0 1 0 1 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]1 1 0 1 1[/B][/TD] [TD]1 0 1 1 0 1 1 0 0 1[/TD] [/TR] [TR] [TD][B]1 1 1 0 0[/B][/TD] [TD]1 1 0 0 0 1 0 0 0 0[/TD] [/TR] [TR] [TD][B]1 1 1 0 1[/B][/TD] [TD]1 1 0 1 0 0 1 0 0 1[/TD] [/TR] [TR] [TD][B]1 1 1 1 0[/B][/TD] [TD]1 1 1 0 0 0 0 1 0 0[/TD] [/TR] [TR] [TD][B]1 1 1 1 1[/B][/TD] [TD]1 1 1 1 0 0 0 0 0 1[/TD] [/TR] [/TABLE] [B]Observations from Truth Table:[/B] [TABLE="width: 624, align: left"] [TR] [TD][B]y[SUB]i[/SUB][/B][/TD] [TD][B]y[SUB]i [/SUB]in terms of x[/B][/TD] [/TR] [TR] [TD][B]y[SUB]0[/SUB][/B][/TD] [TD]x[SUB]0[/SUB][/TD] [/TR] [TR] [TD][B]y[SUB]1[/SUB][/B][/TD] [TD]0[/TD] [/TR] [TR] [TD][B]y[SUB]2[/SUB][/B][/TD] [TD]x[SUB]1*[/SUB]x[SUB]0[/SUB]’[/TD] [/TR] [TR] [TD][B]y[SUB]3[/SUB][/B][/TD] [TD]x[SUB]0 [/SUB]* (x[SUB]1 [/SUB]xor x[SUB]2[/SUB]) = x[SUB]0[/SUB]* (x[SUB]1[/SUB]x[SUB]2[/SUB]’ + x[SUB]1[/SUB]’x[SUB]2[/SUB])[/TD] [/TR] [TR] [TD][B]y[SUB]4[/SUB][/B][/TD] [TD](x[SUB]2 [/SUB]+ x[SUB]3[/SUB]) * (x1 * x2' )' = (x[SUB]2[/SUB] + x[SUB]3[/SUB])*( x[SUB]1[/SUB]’ + x[SUB]2[/SUB])[/TD] [/TR] [TR] [TD][B]y[SUB]5[/SUB][/B][/TD] [TD][/TD] [/TR] [TR] [TD][B]y[SUB]6[/SUB][/B][/TD] [TD][/TD] [/TR] [TR] [TD][B]y[SUB]7[/SUB][/B][/TD] [TD][/TD] [/TR] [TR] [TD][B]y[SUB]8[/SUB][/B][/TD] [TD][/TD] [/TR] [TR] [TD][B]y[SUB]9[/SUB][/B][/TD] [TD][/TD] [/TR] [/TABLE] [B]Switching functions for each y[SUB]i[/SUB][/B] As you can see, I've completed the truth table for y = x^2. I've also derived y0... y4. It's apparent that y0 = x0 and that y1 will always equal 0... etc. Beyond y4, I cannot see how any of them concretely relate to the given x inputs. This is the issue. I'm looking for help in the form of prior knowledge or links to relevant information. I did my fair share of Google'ing and wasn't able to find anything relevant, and I am truly and genuinely stuck. Thank you in advance for any help at all! P.S. I didn't know for sure if this actually belonged in Hardware/Software.
x^5
I don't even..
This looks like a lot of fun...
Im Logic Studio and I dont have a clue
Sorry, you need to
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