How does one form an equation for adder/subtractor?

[AilingLore21]

I understand the concept of Kmaps, Quine method and forming a logic diagram but I'm lost at forming an equation from an addition and subtraction equation

For example: a 2 bit plus a 3 bit binary integer. I would have a 4 bit sum and 3 carries. However, how does one form the appropriate equation in order to convert it to a proper logic circuit?

 

[berkeman]

I understand the concept of Kmaps, Quine method and forming a logic diagram but I'm lost at forming an equation from an addition and subtraction equation

For example: a 2 bit plus a 3 bit binary integer. I would have a 4 bit sum and 3 carries. However, how does one form the appropriate equation in order to convert it to a proper logic circuit?

Write a truth table for each output based on the inputs. Then do a K-map for each of the outputs and design the logic from the minterms... Can you show us what you have been reading about how to do this?

 

[Svein]

Study http://www.slideshare.net/umairsimjee/half-adder-full-adder.

 

[AilingLore21]

Study http://www.slideshare.net/umairsimjee/half-adder-full-adder.

Doesn't explain how subtraction works. What I don't get is why does three inputs of 1 yields an output of 1 carry and 1 sum?

 

[AilingLore21]

Write a truth table for each output based on the inputs. Then do a K-map for each of the outputs and design the logic from the minterms... Can you show us what you have been reading about how to do this?

So these sites currently

:http://orimath.blogspot.com/2008/01/half-adder-full-adder-and-multiple-bit.html
http://www.electronics-tutorials.ws/combination/comb_7.html
http://www.allaboutcircuits.com/textbook/digital/chpt-9/full-adder/

Nobody explains how the truth table for multiple bits work. I assume they're half adders and full adders clumped together but how to form an equation from it? Like where did the AND gate come from? And why put the AND gate for the carries separately instead of putting it in one 3 input AND gate for the 3 bit addition?

 

[Svein]

Doesn't explain how subtraction works. What I don't get is why does three inputs of 1 yields an output of 1 carry and 1 sum?

The answer to both questions: Write up the addition and subtraction tables completely with carry and borrow. Then deduce the logical gate combination.

Nobody explains how the truth table for multiple bits work.

Oh, yes they do. Start with https://en.wikipedia.org/wiki/Truth_table