In a certain number system, the number '101' represents the decimal number 5. Wh

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Question: In a certain number system, the number \'101\' represents the decimal number 5. What does \'111\' represent in the same system?

Options:

Correct Answer: 7

Solution:

\'101\' in binary is 5, so \'111\' in binary is 7.

In a certain number system, the number '101' represents the decimal number 5. What does '111' represent in the same system?

In a certain number system, the number '101' represents the decimal number 5. What does '111' represent in the same system?

Step 1: Understand that '101' is a number in a certain number system, which is binary (base 2).
Step 2: Convert '101' from binary to decimal. In binary, '101' means: 1*2^2 + 0*2^1 + 1*2^0 = 4 + 0 + 1 = 5.
Step 3: Now, we need to find out what '111' represents in the same binary system.
Step 4: Convert '111' from binary to decimal. In binary, '111' means: 1*2^2 + 1*2^1 + 1*2^0 = 4 + 2 + 1 = 7.
Step 5: Therefore, '111' in this number system represents the decimal number 7.

Number Systems – Understanding how different number systems (like binary) represent decimal values.
Binary Representation – Converting binary numbers to decimal and vice versa.