This is a simplified 4x4 bit version, and it goes sort of like this:ġ) The 4-bit multiplier is loaded and stored in the P shift register, specifically Pl. I leared shift registers, ALUs, and all that by the end of my first digital logic course. This may be a little more difficult so don't worry about understanding how each of the components works underneath, because you will learn it soon. Some processors though have even faster multiply implementations that make use of wallace treesĪlso, if you'd like a little more insight on the sequential type multiplier, here you go. That is the absolute most simplistic method of performing the multiplication sequentially. Finally, they add all of the partial sums together. Instead, as the wikipedia article you read states, they multiply one of the 64-bit operands by each individual bit of the 2nd operand, each time shifting the result.

For instance on a 64-bit computer, the amount of combinational logic necessary to perform 64圆4 bit multiplication would be insane. Real processors and the ALUs inside of them don't exactly do it this way. And voila, you have a circuit that performs binary multiplication. Now I just need to throw in the logic gates to match those equations. In this case, I let this handy program do it for me.Īt this point, you can see that I have an equation for F0 through F3 based on the inputs. In decimal, that's just 3 * 3 = 9Īfter the truth table is complete, you could fill this into a karnaugh map, and derive the equations for each output of the circuit. Sorry, it's backwards as typically the LSB is A0 or B0, I numbered it wrong. Go through each row, and you'll see how it implements it. For 2x2 bit multiplication, this is the truth table: If you're a EE/CPE student and you're just starting to learn logic, maybe you haven't learned this yet but you will.Īrithmetic and logic functions are essentially realized in circuit form by starting with a truth table and filling in the values that implement the function you want.

3 bit multiplier