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 \'110\' represent in the same system?

Options:

Correct Answer: 7

Solution:

\'101\' in binary is 5 in decimal. \'110\' in binary is 6 in decimal.

In a certain number system, the number '101' represents the decimal number 5. What does '110' represent in the same system?

In a certain number system, the number '101' represents the decimal number 5. What does '110' 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, which equals 4 + 0 + 1 = 5.
Step 3: Now, we need to convert '110' from binary to decimal. In binary, '110' means 1*2^2 + 1*2^1 + 0*2^0.
Step 4: Calculate the value of '110' in decimal: 1*2^2 = 4, 1*2^1 = 2, and 0*2^0 = 0. So, 4 + 2 + 0 = 6.
Step 5: Therefore, '110' in this number system represents the decimal number 6.

Binary Number System – Understanding how binary numbers are converted to decimal values.