Question

How do I check numbers that are valid for each bases ?

Please show the method and specify steps

4. Which of the following would be valid numbers for bases 3, 7, 8, 13, 15 and 16? a. DEADBEAF b. DC4A c. 122 d. 1689 e. 1337 f. 888

Answer 1

in a number system which has a base b then the digits in the number system will be from 0 to (b-1)

lets the popular base system 10 the digits will be 0,1,2,3,4,5,6,7,8,9 and any number after that are formed using the digits from 0-9

in a binary system, the digits will be either 0 or 1 since its base 2 digits will be 0,1

we have a base system 12 then the digits should be 0,1,2,3,4,5,6,7,8,9,A,B

a)DEADBEAF since the largest digit is F, the number belongs to the base 16, any system below 16 will not have F in their number system

b)DC4A since the largest digit is D, the number is valid in all the number system above base 13 (i.e 14,15,16,..........)

so DC4A belongs to 15,16

c)122 since the largest digit is 2, the number is valid in all the number system above base 2 (i.e 3,4,5,6,7,8,9,.........)

so 122 belongs to 3,7,8,13,15,16

d)1689, since the largest digit is 9, the number is valid in all the number system above base 9 (i.e 10,11,12,13,.........)

so 1689 belongs to 13,15,16

e)1337 since the largest digit is 7, the number is valid in all the number system above base 7 (i.e 8,9,10,11,,,.........)

so 1337 belongs to 8,13,15,16

f)888  since the largest digit is 8, the number is valid in all the number system above base 8 (i.e 9,10,11,.........)

so 888 belongs to 13,15,16