Karnaugh Map for 4-bit Multiplication: How to Determine Values for Clusters?

[mmmboh]

Make a circuit to multiply two 2-bit numbers
AB and CD together to produce a 4-bit output.
(a) construct a truth table to represent all states of the inputs and
the corresponding outputs.
(b) make a Karnaugh map for each output bit. Write down the Boolean algebraic expressions that describe the clusters in each map.
(c) design a logic circuit for each output bit to perform the multiplication.

Ok well I am on part b, I have done the truth table already, but I have one problem when making the Karnaugh map, how do I know when to put a 0 or 1 in a place, like if they output is 0000, I guess I put a 0, but if it's something like 0110, do I put a 0 or a 1? I don't understand how I am suppose to know which numbers are high and low, can someone help please? thanks!

For example the truth table here, http://en.wikipedia.org/wiki/Karnaugh_map#Truth_table", how do they know what f(A,B,C,D) is?

Truth table:

A(1) A(0) B(1) B(0) C(3) C(2) C(1) C(0)

0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 0 1 0 0 0 1
0 1 1 0 0 0 1 0
0 1 1 1 0 0 1 1
1 0 0 0 0 0 0 0
1 0 0 1 0 0 1 0
1 0 1 0 0 1 0 0
1 0 1 1 0 1 1 0
1 1 0 0 0 0 0 0
1 1 0 1 0 0 1 1
1 1 1 0 0 1 1 0
1 1 1 1 1 0 0 1

 

[berkeman]

Make a circuit to multiply two 2-bit numbers
AB and CD together to produce a 4-bit output.
(a) construct a truth table to represent all states of the inputs and
the corresponding outputs.
(b) make a Karnaugh map for each output bit. Write down the Boolean algebraic expressions that describe the clusters in each map.
(c) design a logic circuit for each output bit to perform the multiplication.

Ok well I am on part b, I have done the truth table already, but I have one problem when making the Karnaugh map, how do I know when to put a 0 or 1 in a place, like if they output is 0000, I guess I put a 0, but if it's something like 0110, do I put a 0 or a 1? I don't understand how I am suppose to know which numbers are high and low, can someone help please? thanks!

For example the truth table here, http://en.wikipedia.org/wiki/Karnaugh_map#Truth_table", how do they know what f(A,B,C,D) is?

Truth table:

A(1) A(0) B(1) B(0) C(3) C(2) C(1) C(0)

0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 0 1 0 0 0 1
0 1 1 0 0 0 1 0
0 1 1 1 0 0 1 1
1 0 0 0 0 0 0 0
1 0 0 1 0 0 1 0
1 0 1 0 0 1 0 0
1 0 1 1 0 1 1 0
1 1 0 0 0 0 0 0
1 1 0 1 0 0 1 1
1 1 1 0 0 1 1 0
1 1 1 1 1 0 0 1

You make a K-map for each of the 4 output bits, and use the 4 input bits to label the rows and columns. Then for each entry, you use the output bit value to fill in the square that corresponds to the input code.

 

[berkeman]

BTW, one tip for putting tables in your posts is to use the "code" tags. That makes the forum use non-proportional font, so things stay lined up in the columns you typed them in.