If the base of a number system is increased by 1, how does the representation of the number '10' change?
Practice Questions
1 question
Q1
If the base of a number system is increased by 1, how does the representation of the number '10' change?
It remains the same
It becomes 11
It becomes 1
It becomes 2
In base 'b', '10' represents 'b'. In base 'b+1', it becomes '11'.
Questions & Step-by-step Solutions
1 item
Q
Q: If the base of a number system is increased by 1, how does the representation of the number '10' change?
Solution: In base 'b', '10' represents 'b'. In base 'b+1', it becomes '11'.
Steps: 5
Step 1: Understand what a base is. A base (or radix) is the number of unique digits, including zero, used to represent numbers in a positional numeral system.
Step 2: In base 'b', the number '10' means '1' times 'b' plus '0' times '1', which equals 'b'.
Step 3: If we increase the base by 1, we have 'b + 1'.
Step 4: In base 'b + 1', the number '10' now represents '1' times '(b + 1)' plus '0' times '1', which equals 'b + 1'.
Step 5: The representation of 'b' in base 'b + 1' is '11', because '1' times '(b + 1)' is 'b + 1' and '0' times '1' is still '0'.
