In the binary number 100000, what weight does the "1" carry?

In the binary number 100000, what weight does the "1" carry?

• A. 16
• B. 8
• C. 32
• D. 64

Answer: (C)

In the binary number system, each digit represents a power of two, starting from the rightmost digit, which is 2^0. In the binary number 100000, the "1" is located in the sixth position from the right, which corresponds to 2 raised to the power of 5. Calculating this gives: 2^5 = 32. Thus, the "1" in the binary number 100000 carries a weight of 32. This means that the presence of the digit "1" in that particular position contributes 32 to the overall value of the binary number. Understanding the positional weight in binary is crucial as it forms the foundation for both binary arithmetic and number representation in digital systems.

In the binary number system, each digit represents a power of two, starting from the rightmost digit, which is 2^0. In the binary number 100000, the "1" is located in the sixth position from the right, which corresponds to 2 raised to the power of 5.

Calculating this gives:

2^5 = 32.

Thus, the "1" in the binary number 100000 carries a weight of 32. This means that the presence of the digit "1" in that particular position contributes 32 to the overall value of the binary number. Understanding the positional weight in binary is crucial as it forms the foundation for both binary arithmetic and number representation in digital systems.