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In a certain number system, the number '101' represents the decimal number 5. Wh
In a certain number system, the number '101' represents the decimal number 5. What does '111' represent in the same system?
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Q1
In a certain number system, the number '101' represents the decimal number 5. What does '111' represent in the same system?
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'101' in binary is 5, so '111' in binary is 7.
Questions & Step-by-step Solutions
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Q
Q: In a certain number system, the number '101' represents the decimal number 5. What does '111' represent in the same system?
Solution:
'101' in binary is 5, so '111' in binary is 7.
Steps: 5
Show Steps
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.
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