Question

Envision a base-5 numbering system. Write the rules for the system, and give six 3-digit examples in base-5 with their equivalent decimal and binary values.

Answer 1

See Explanation Section

Explanation:

Given

A base 5 numbering system: Envision

Some of the rules are as follows:

1. For a base 5 system, the highest individual digit is 4: Meaning that the 1234, 343, 110 are valid digits while 1235, 78, 55 are invalid digits
2. The place values of this system are in place of 5s: i.e. ......5°, 5¹, 5², 5³, 5⁴......

3 digit examples

1

Base 5: 100

Base 10: 25 (See calculation below)

`1 * 5^2 + 0 * 5^1 + 0 * 5^0 = 1 * 25 + 0 + 0 = 25`

Base 2: 11001 (See calculation below)

`25 / 2 = 12\ R\ 1`

`12 / 2 = 6\ R\ 0`

`6 / 2 = 3\ R\ 0`

`3 / 2 = 1\ R\ 1`

`1 / 2 = 0\ R\ 1`

Writing the remainder from bottom: 11001

Using the same steps as used in (1) above

2.

Base 5: 211

Base 10: 56

Base 2: 111000

3.

Base 5: 441

Base 10: 121

Base 2: 1111001

4.

Base 5: 230

Base 10: 65

Base 2: 1000001

5.

Base 5: 342

Base 10: 97

Base 2: 1100001

6.

Base 5: 141

Base 10: 46

Base 2: 101110