Question

Can someone help me Convert the following from the base indicated, to the base requested.

(4.1) 14 base 10 = ?? base 3


(4.2) B2 base 16= ?? base 2

Answer 1

Sure, I can help you with that.

(4.1) 14 base 10 = 1102 base 3

To convert a number from base 10 to base 3, we repeatedly divide the number by 3 and write down the remainders. The remainders are read from right to left to form the number in base 3.

14 / 3 = 4 with remainder 2

4 / 3 = 1 with remainder 1

Therefore, 14 in base 10 is equal to 1102 in base 3.

(4.2) B2 base 16 = 10110010 base 2

To convert a number from base 16 to base 2, we repeatedly divide the number by 2 and write down the remainders. The remainders are read from right to left to form the number in base 2.

B2 / 2 = 51 with remainder 0

51 / 2 = 25 with remainder 1

25 / 2 = 12 with remainder 1

12 / 2 = 6 with remainder 0

6 / 2 = 3 with remainder 0

3 / 2 = 1 with remainder 1

Therefore, B2 in base 16 is equal to 10110010 in base 2.

Step-by-step explanation:

Answer 2

Certainly! Here are the steps to convert the given numbers from one base to another:

1. Converting (4.1) from base 10 to base 3:

`(4.1)_(10)` = ?? base 3

To convert a number from base 10 to base 3, we need to divide the number successively by 3 and record the remainders until the quotient becomes zero. Then, we read the remainders in reverse order to get the equivalent number in base 3.

Here are the steps:

Step 1: Divide 14 by 3

`\left\lfloor (14)/(3) \right\rfloor = 4` (quotient)

`14 \mod 3 = 2` (remainder)

Step 2: Divide 4 by 3

`\left\lfloor (4)/(3) \right\rfloor = 1` (quotient)

`4 \mod 3 = 1` (remainder)

Step 3: Divide 1 by 3

`\left\lfloor (1)/(3) \right\rfloor = 0` (quotient)

`1 \mod 3 = 1` (remainder)

Since the quotient is now 0, we stop. The remainders in reverse order are 112. Therefore, (4.1) base 10 is equivalent to
`(112)_3`.

2. Converting (4.2) from base 16 to base 2:

`(4.2)_(16)` = ?? base 2

To convert a number from base 16 to base 2, we need to convert each digit of the number from base 16 to base 2.

Here are the steps:

Step 1: Convert the digit B to base 2

B in base 16 is equal to 1011 in base 2.

Step 2: Convert the digit 2 to base 2

2 in base 16 is equal to 0010 in base 2.

Combining the converted digits, we get
`(4.2)_(16) = (1011.0010)_2` in base 2.

`\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}`

♥️
`\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}`