Questions on Number bases?

hi everyone,


i need help to solve these questions. I found these questions in a book with no answer sheet and I'm kinda new to these kind of questions. please guide me through these questions with calculation steps. thanks.





Given that 10011 (base 2) - P (base 2) = 1101 (base 2)





a) find the value of P,


b) express P as a number in base five,


c) express P as a number in base eight.

Questions on Number bases?
a.) p = 6 (In Decimal ie base 10)


b.) Base 5 p = 11


c.) Base 8 p = 6
Reply:a) 110





You can do it by converting the numbers to base 10:





10011 = 19 and 1101 = 13 so P = 6





I base 2, 6 = 4 + 2





In base 2, 4 = 100 and 2 = 10 so 100 + 10 = 110





You can also do it directly:





from the right hand side, 1 - 1 = 0 so last digit is 0





next one in: 1 - 0 = 1 so second to last digit is 1





next one: 0 - 1 is 1, but have to pay back by ading 1 in next column, so you get 10 - 10 whih is 0





thus answer is 110





b)





In base 10 the number is 6, so in base 5 it is 5^1 + 1 = 11





c) in base 8 the number will be 6 because it is less than 8

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