In decimal, a 3-bit binary number can represent how many different numbers?

In decimal, a 3-bit binary number can represent how many different numbers?

• A. 6
• B. 7
• C. 8
• D. 9

Answer: (C)

A 3-bit binary number can represent different values through the combination of its bits, where each bit has two possible states: either 0 or 1. Since each bit can be in one of two states, the total number of different combinations that can be created with 3 bits is calculated using the formula \(2^n\), where \(n\) is the number of bits. For a 3-bit number, this becomes \(2^3\). The calculation yields 8, which represents the possible combinations: - 000 (0 in decimal) - 001 (1 in decimal) - 010 (2 in decimal) - 011 (3 in decimal) - 100 (4 in decimal) - 101 (5 in decimal) - 110 (6 in decimal) - 111 (7 in decimal) Each of these combinations corresponds to a unique decimal value, illustrating that a 3-bit binary system can represent 8 different numbers, ranging from 0 to 7 in decimal notation.

A 3-bit binary number can represent different values through the combination of its bits, where each bit has two possible states: either 0 or 1. Since each bit can be in one of two states, the total number of different combinations that can be created with 3 bits is calculated using the formula (2^n), where (n) is the number of bits.

For a 3-bit number, this becomes (2^3). The calculation yields 8, which represents the possible combinations:

• 000 (0 in decimal)

• 001 (1 in decimal)

• 010 (2 in decimal)

• 011 (3 in decimal)

• 100 (4 in decimal)

• 101 (5 in decimal)

• 110 (6 in decimal)

• 111 (7 in decimal)

Each of these combinations corresponds to a unique decimal value, illustrating that a 3-bit binary system can represent 8 different numbers, ranging from 0 to 7 in decimal notation.