boolean help. adder and subtractor

david90

A boolean circuit has 4 inputs, a, b, cin and K. when K=0, the circuit is an adder. When K=1, the ciruit is a subtractor. WHere do I start? [o)] [*(] [g)] [?]

Hurkyl

Depends on what you're trying to do and what you already know. I imagine you want the circuit for your adder/subtractor, right?

There are lots of ways to go:

You could build an adder, a subtractor, and a chooser circuit.

You could make a truth table and build the circuit from that.

You could analyze the difference between the circuits of an adder and a subtractor and hack it to provide the toggling capability.

david90

i'm not trying to make a REAL circuit, I just need to know the boolean equation and schematic. I already know what full adder and subtractor look like. I just don't know how to toggle between the two with a 4th input K.

Hurkyl

Well, my post still applies if you replace "circuit" with "formula".

david90

not helping[*(]

Guybrush Threepwood

The inputs a and b are they 1 bit or buses?

Hurkyl

Well, there are two cases, right?

K is false and the formula gives the output of an adder
or
K is true and the formula gives the output of a subtractor

david90

still not helping. ur just restating my question. I already know there are 2 cases and that k=0 then it is an adder.

chroot

Consider the naive approach: multiplex the outputs of each, as Hurkyl said.

A two-bit multiplexor looks like this:

(m & s) | (n & ~s)

where & is AND, | is OR, and ~ is NOT. m and n are the two inputs, and s is the select signal.

Does this make sense?

If you want to make the simplest possible formula, replace m and n with the formulas for a 1-bit adder and a 1-bit subtractor. Finally, do all the boolean simplification you can.

Another approach would be to write out a truth table for the whole design -- a K-map -- and do the normal K-map stuff to get the equation.

- Warren

Hurkyl

There's something special about the way I restated your question; it's directly translatable into a formula!


Is the same as

(~K & (formula for adder)) | (K & (formula for subtractor))

david90

Thanks i kinda get it now. what is "~"?

Guybrush Threepwood

it is another way of saying not...
~a = !a = not(a)

david90

not is an inverter right?

chroot

Yes, it's an inverter. David, you seem to be completely unprepared to handle this problem. Why? Are you in a class where this was asked? Are you not paying any attention to the lectures?

- Warren

Janus

Here, I'll give you a hint to get you started:

Think "2's compliment subtraction"

david90

I have been paying attention in class. It is just that my prof. cares so much about me and the students about getting a job after grad. that he teaches some extra stuff that we're not suppose to learn in ece 204. I'm not sure if I should cuss him out or thank him.[g)]

david90

what is a weighted code (BCD related) and how does it relates to gray code?