Is there an algorithmic or easier way to design circuits with components such as half adders, full adders, etc?

I find that the "traditional" combination circuits are a lot more easier to implement because I could just list out the truthtable and then go through some K-Map or boolean algebra process to get a boolean equation and can know what logic gates to use to implement the function from that equation.

But when asked to implement circuits with components such as half-adders, full-adders, comparators, etc, I am always stuck! I don't seem to have any hindsight on these problems. Say for a simple circuit to convert 4-bit Grey Code to 4bit binary code with half-adders, I couldn't see how and where I should start from. Trying every possible ways to connect the circuit would take up too much time too.

So is there an easier or cleverer way to do up these circuits especially with adders other than trying every possible ways?

Thanks!

 

I don't think non-straightforward problems in digital electronics have a standard solution. You have to put your back into finding a modular and scalable solution to fit your needs. Noone said it would be easy.
Your only help is that mostly anything that you want to build was already been built before, and probably has left some schematics behind it.

Anyway, single ICs aren't the way to go when you try to design complex circuitry. Either find a microcontroller and program it to your needs or if you are a buzzillion dollar company you will make your own processor. There, the bibliography describing common practices and simplification theory is quite extensive.

 

Actually, usually they are just simple circuits. Circuits as simple as converting grey code to binary code. But when asked to use only half-adder, I am totally dumbfounded. I don't know where to start from. It is not like the kind of combinational circuits which you know you could start collecting the minterms and then do a boolean algebra to get the equation to set up the circuit with the logic gates according to the boolean expression. When asked to design and draw circuit diagrams with modular components such as half-adder, I am always stuck right at the beginning even for simple circuits like converting grey code to binary. It's like I know how grey code and binary code look like and their difference and visual pattern. But implementing a circuit to convert between them with half-adder is like "woah! where do I even start from?!"

 

Can you post an exact question if you have one, so that we can talk over something specific?

 

Here's one of the kind of questions:
A function F(a,b,c,d,e) is defined as a a function which return "1" if there are exactly 2 1-bits in a 5 bit code and return "0" otherwise.
Given a 4-bit magnitude comparator, a 2-bit parallel adder and some half-adders, without any other device or logic gate, implement the function F.

So I started by listing all the possible code values:
00011
00110
00101
01100
01010
01001
11000
10100
10010
10001

After which, I have no idea where to continue from and I would usually get stuck. Is there a systematic way to tackle these problems?

 

I 'll choose to take advantage of the rules and interpret some as "as many as I want".

I would sum all of the bits of the number. I could use the 2-bit parallel adder for the first 4 (3 bit result), and another 3-bit full adder made from half adders to add the last bit, the MSB. The result is 4 bits.

I would then use the comparator to compare the result with the number 2. The function F is the "=" output of the comparator.


It is true that this kind of problems don't have any formal way of solution. You need good understanding of the parts you have and some quiz solving skills to tackle them.

 

ahh! that's pretty smart. i thought this is really a good way to think about the problem.

yea you are right. I need to be more famiiliar with the parts to come out of the solution.

thanks!