Question

In how many number systems are there exactly 2097152 different numbers, up to 7 digits?

a) 8

b) 16

c) 2

d) 10

Answer 1

The number of different number systems where there can be exactly 2,097,152 different numbers with up to 7 digits is one: the base 8 number system.

Step-by-step explanation:

The question asks in how many number systems there are exactly 2,097,152 different numbers, up to 7 digits.

To solve this problem, you need to know that the number of different numbers that can be represented by a 7-digit number in any base (or radix) number system is equal to the base raised to the power of the number of digits.

So, our equation looks like base7 = 2,097,152.

You can solve this with a logarithm or recognizing that 2,097,152 is a power of 2, specifically 221. Since we want the base to the power of 7 to equal to 221, the base needs to be 23 because (23)7 = 2(3*7) = 221.

Therefore, 23 equals 8, and the base is 8.