Engineering Combinational circuit that multiplies two numbers together

[Ramir]

Homework Statement

Design a combinational circuit that multiplies two numbers together, and outputs the result.

Homework Equations

The biggest product will be 3 * 3 = 9.

Four bits to represent the product.

0: 00
1: 01
2: 10
3: 11

I need a 4 bit register for the outputs

The Attempt at a Solution

The biggest product will be 3 * 3 = 9.
Four bits to represent the product.
0: 00
1: 01
2: 10
3: 11

I need a 4 bit register for the outputs, right?

How do I start my truth table? like this?

A B C D | Output | AB | CD

How will I form the expressions from the truth table?
I know how to solve with a K-map, but I'm having a hard time visualizing and building it.

 

[berkeman]

A B C D | Output | AB | CD

Welcome to the PF.

I don't think you need the last part of the above -- what is it meant to represent?

Just fill out the truth table with the 2x2-bit inputs and the resulting 4-bit output. Then do a K-map for each of the 4 output bits versus the 4 input bits. Can you show us that truth table?

Hint -- use the [ code ] and [ /code ] tags (without the spaces) around your truth table to enforce uniform spacing of the characters so the columns line up.

 

[Ramir]

Okay I uploaded a picture. I put the 1's in the K-map after and now i need to form the expression. I build the circuit from the expression then?

 

[berkeman]

That table doesn't make any sense to me.

The Truth Table for this 2-bit multiplier should have 4 columns of input bits and 4 columns of output bits. The output bits for each row are the binary result of multiplying the two 2-bit input binary numbers.

Try again?

 

[Ramir]

I uploaded another.. I don't understand how to get the highs in the x,y,z outputs though, what am I looking at to form the logic?

 

[berkeman]

Much better!

So now you design 4 logic circuits, one each for the W, X, Y and Z outputs. The 4 inputs (A, B, C, D) go into each of the combinatorial circuits.

Use 4 K-maps to design the 4 logic circuits. Can you show us your try at the 4 K-maps?

 

[Ramir]

Here's a look at my K-Map and expressions. Now I take the expressions and build the circuit in a testing program?

 

[berkeman]

Great! I checked the K-maps and they look right for W, X, Y and Z (from top to bottom -- they should be labeled).

And yes, now just write down the circuits that correspond to those minterms. Good work.

 

[Ramir]

Thanks for your help, appreciated greatly! I never turned a big expression like B'CD + A'BD + BCD + ABD + DB into a circuit before. Do I take the expressions for w,x,y,z and put them altogether?

 

[berkeman]

Do I take the expressions for w,x,y,z and put them altogether?

No, you will make 4 separate circuits; one each for the W, X, Y, and Z output bits for the multiplier. You make each circuit with inverters, AND gates and OR gates (that's one way to implement minterms anyway).

 

[Ramir]

Can you help me set one up, preferably a harder one?

AC'D+ AB'D + BCD' + A'BC

 

[Ramir]

Will I have three Or's in that expression?

 

[berkeman]

Can you help me set one up, preferably a harder one?

AC'D+ AB'D + BCD' + A'BC

Will I have three Or's in that expression?

Yes. Sorry for the delay in responding.

You implement that with inverters, AND gates, and OR gates. For the terms like C', use an inverter to make C' from the C input. For terms like AC'D, use a 3-input AND gate. And then use OR gates to implement the "+" operations.