How many states can a 3-bit binary number represent?

How many states can a 3-bit binary number represent?

• A. 4 states
• B. 6 states
• C. 8 states
• D. 16 states

Answer: (C)

A 3-bit binary number can represent various combinations of binary states. Each bit in a binary number can have two possible values: 0 or 1. Therefore, the total number of different states that can be represented by a binary number can be calculated using the formula \(2^n\), where \(n\) is the number of bits. In the case of a 3-bit binary number: - \(n = 3\) - The calculation is \(2^3 = 8\). Thus, a 3-bit binary number can represent a total of 8 different states, which can be enumerated as follows: 000, 001, 010, 011, 100, 101, 110, and 111. Each of these combinations corresponds to a unique value ranging from 0 to 7 in decimal form. Therefore, it is clear why the answer C, indicating 8 states, is the correct choice.

A 3-bit binary number can represent various combinations of binary states. Each bit in a binary number can have two possible values: 0 or 1. Therefore, the total number of different states that can be represented by a binary number can be calculated using the formula (2^n), where (n) is the number of bits.

In the case of a 3-bit binary number:

• (n = 3)

• The calculation is (2^3 = 8).

Thus, a 3-bit binary number can represent a total of 8 different states, which can be enumerated as follows: 000, 001, 010, 011, 100, 101, 110, and 111. Each of these combinations corresponds to a unique value ranging from 0 to 7 in decimal form. Therefore, it is clear why the answer C, indicating 8 states, is the correct choice.