K Map Help: Finding Minterms for Reordered Expression F(C,B,A,D)

[physics=world]

1. The original expression is:

F(A,B,C,D) = Σm(0,1,2,5,8,9,10)

If I changed the order of ABCD to:

F(C,B,A,D)

What would be the minterms now?2. Use the truth table for 0 to 15

The Attempt at a Solution

I used the truth table in the regular order

ABCD and for CBAD.ABCD | F
0000 | 1
0001 | 1
0010 | 1
0011 | 0
0100 | 0
0101 | 1
0110 | 0
0111 | 0
1000 | 1
1001 | 1
1010 | 1
1011 | 0
1100 | 0
1101 | 0
1110 | 0
1111 | 0

So, here I basically thought that if C was 1 in the regular column then in the new truth table I just look for 1 under the C column. Is this right or do I need to redo the columns so that everything under the A column from the regular truth table is shifted over to 2 columns over?

CBAD | F
0000 | 1
0001 | 1
0010 | 1
0011 | 1
0100 | 0
0101 | 1
0110 | 0
0111 | 0
1000 | 1
1001 | 0
1010 | 1
1011 | 0
1100 | 0
1101 | 0
1110 | 0
1111 | 0

I got F(C,B,A,D) = Σm(0,1,2,3,5,8,10)

is this correct? I thought that if you changed the order than the minterms should change and only one minterm changed.

 

[KataKoniK]

Hello,
You are correct in your approach. When you change the order of the variables in the function, the minterms will also change. In this case, the minterms will be:

F(C,B,A,D) = Σm(0,1,2,3,5,8,10)

This is because the minterms are based on the binary representation of the variables, and when you change the order, the binary representation also changes. So, it is important to change the columns accordingly when creating the truth table.
Your method of looking for 1 under the C column is correct. Keep in mind that the order of the minterms may not always change when you change the order of the variables. It will depend on the function and the order in which the variables are changed.
I hope this helps. Let me know if you have any other questions.