Question

How many 8-bit binary numbers ( 0 s and 1 s) contains exactly two zeros? (This is similar to consider 8 coins and asking how many ways we can have 2H and 61 exactly?) a. 20160 b. 28 c. 56 d. 40320 e. 4

Answer 1

Therefore, the number of 8-bit binary numbers that contain exactly two zeros is 28.

Among the provided answer choices, option (b) correctly corresponds to the answer: 28.

Explanation:

To determine the number of 8-bit binary numbers that contain exactly two zeros, we need to calculate the number of ways we can choose the positions for the two zeros.

Step 1: Select the positions for the two zeros.

We have 8 positions in total, and we need to choose 2 of them for the zeros. This can be calculated using combinations: C(8, 2) = 8! / (2! * (8-2)!) = 28.

Step 2: Determine the number of ways to fill the remaining 6 positions with ones.

Since the remaining 6 positions should be filled with ones, there is only one way to do so.

Step 3: Multiply the results of both steps.

To find the total number of 8-bit binary numbers with exactly two zeros, we multiply the results of both steps together:

28 * 1 = 28.