Question
Look at the truth table below. A, B, and C are inputs and Z
is the output. How many cells must its Karnaugh Map
contain?
A B C Z
0 0 1 1 0 0 1
1 0 0 0 0 1 1 1
1
0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1
is the output. How many cells must its Karnaugh Map
contain?
A B C Z
0 0 1 1 0 0 1
1 0 0 0 0 1 1 1
1
0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1
Answers
GPT-4o mini
To determine how many cells a Karnaugh Map (K-map) must contain for the given truth table, we need to identify the number of variables and understand how a K-map is structured.
In your truth table, the inputs are A, B, and C. This gives us:
- A = 1 bit
- B = 1 bit
- C = 1 bit
Since there are 3 variables (A, B, and C), a K-map for 3 variables will have \(2^3 = 8\) cells. Each cell in the K-map corresponds to a unique combination of the input variables, and since our inputs are all binary (0 or 1), we will cover all combinations from 000 to 111.
Therefore, the K-map will contain **8 cells**.
In your truth table, the inputs are A, B, and C. This gives us:
- A = 1 bit
- B = 1 bit
- C = 1 bit
Since there are 3 variables (A, B, and C), a K-map for 3 variables will have \(2^3 = 8\) cells. Each cell in the K-map corresponds to a unique combination of the input variables, and since our inputs are all binary (0 or 1), we will cover all combinations from 000 to 111.
Therefore, the K-map will contain **8 cells**.