In a number system, if '100' represents 4, what does '110' represent?
Practice Questions
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Q1
In a number system, if '100' represents 4, what does '110' represent?
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'100' in base 4 is 4. '110' in base 4 is 1*16 + 1*4 + 0 = 20, which is 6.
Questions & Step-by-step Solutions
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Q
Q: In a number system, if '100' represents 4, what does '110' represent?
Solution: '100' in base 4 is 4. '110' in base 4 is 1*16 + 1*4 + 0 = 20, which is 6.
Steps: 7
Step 1: Understand that '100' represents the number 4 in a certain base system.
Step 2: Identify the base of the number system. Since '100' equals 4, we can deduce that it is in base 4.
Step 3: Convert '110' from base 4 to decimal. In base 4, each digit represents a power of 4.
Step 4: Break down '110' in base 4: The leftmost '1' is in the 4^2 place, the middle '1' is in the 4^1 place, and the rightmost '0' is in the 4^0 place.
Step 5: Calculate the value of each digit: 1 * 4^2 = 1 * 16 = 16, 1 * 4^1 = 1 * 4 = 4, and 0 * 4^0 = 0.
