Karnaugh map and Circuit of a full adder I have the following task: The addition can be implemented by the rules 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10. Full addition requires carry-in and carry-out bits. In general, you must be able to add two terms (bits) a and b, and a carry-in bit Cin to compute a sum bit S and a carry-out bit Cout. a.)Complete the truth table that describes a full adder: The Boolean function that adds two bits A, B, and a carry-in bit Cin to produce a sum bit S and a carry-out bit Cout. b.)Using Karnaugh maps find Boolean expressions that represent the sum function S and the carry-out function Cin. c.)Draw the circuit of the full adder I need help with the second and the third part of the question.

You have two outputs S and Cout so you need to construct a k-map for each of those.

S = f(A,B,Cin)

Cout = g(A, B, Cin)

Our goal is to derive simplified boolean expressions for both the functions f and g. K-maps are quite intuitive once you get the hang of them so I would recommend looking up some examples. Here is a rough idea of how to proceed:

1) label each axis of the table with at most 2 bits and write a separate column/row for each different combination (remember to use gray code).

2) fill in each cell with the corresponding output

3) circle each set of adjacent 1's and derive the boolean expression. This can be found by looking at the at the header and including only the bits that change in the expression.

After you have derived the simplified expressions, constructing the actual circuit can be done directly from the expression.