Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you're looking for. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.

Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$

Sagot :

MrRoyalidn

Complete Question

Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?

The possible values of b are 4 and 5

How to determine the possible numbers of b?

The conditions are given as:

  • b is at least 2
  • When 197 in base b has 4 digits.

So, we start by converting 197 to base 2 and above.

This is done as follows:

197 to base 2

2 | 197

    98 R 1

    49 R 0

    24 R 1

    12 R 0

    6 R 0

    3 R 0

    1 R 1

    0 R 1

So, we have:

197 = 11000101 in base 2

11000101 has more than 4 digits.

This means that b cannot be 2

Using the above method of conversion, we have:

  • 197 = 21022 in base 3
  • 197 = 3011 in base 4
  • 197 = 1242 in base 5
  • 197 = 525 in base 6
  • 197 = 401 in base 7

See that as the base increases, the number of digits decreases.

The numbers in base 4 and 5 have 4 digits.

Hence, the possible values of b are 4 and 5

Read more about base conversions at:

https://brainly.com/question/17946394

#SPJ4

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.