QuestionCalculate the sum: $412_{6}+3121_{6}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are in base6 (denoted by the subscript6) . We are adding two numbers in base63. We need to convert the result to base6 if it exceeds5 (since base6 only has digits from0 to5)

STEP 2

Let's start by adding the numbers in the units place (rightmost digit).
$2_{6} +1_{6}$

STEP 3

Calculate the sum of the units place.
$2_{6} +1_{6} =3_{6}$

STEP 4

Now, let's add the numbers in the tens place (second digit from the right).
$1_{6} +2_{6}$

STEP 5

Calculate the sum of the tens place.
$1_{} +2_{} =3_{}$

STEP 6

Next, let's add the numbers in the hundreds place (third digit from the right).
$4_{6} +1_{6}$

STEP 7

Calculate the sum of the hundreds place.
$4_{6} +1_{6} =5_{6}$

STEP 8

Finally, add the number in the thousands place (fourth digit from the right) to the sum. Since $412_{6}$ doesn't have a thousands place, we only add $3_{6}$ .
$0_{6} +3_{6}$

STEP 9

Calculate the sum of the thousands place.
$_{6} +3_{6} =3_{6}$

STEP 10

Combine the sums of each place to get the final result in base6.
$3_{6}5_{6}3_{6}3_{6}$ The sum of $412_{6}$ and $312_{6}$ in base6 is $3533_{6}$ .

Was this helpful?

QuestionCalculate the sum: $412_{6}+3121_{6}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are in base6 (denoted by the subscript6) . We are adding two numbers in base63. We need to convert the result to base6 if it exceeds5 (since base6 only has digits from0 to5)

STEP 2

Let's start by adding the numbers in the units place (rightmost digit).
$2_{6} +1_{6}$

STEP 3

Calculate the sum of the units place.
$2_{6} +1_{6} =3_{6}$

STEP 4

Now, let's add the numbers in the tens place (second digit from the right).
$1_{6} +2_{6}$

STEP 5

Calculate the sum of the tens place.
$1_{} +2_{} =3_{}$

STEP 6

Next, let's add the numbers in the hundreds place (third digit from the right).
$4_{6} +1_{6}$

STEP 7

Calculate the sum of the hundreds place.
$4_{6} +1_{6} =5_{6}$

STEP 8

Finally, add the number in the thousands place (fourth digit from the right) to the sum. Since $412_{6}$ doesn't have a thousands place, we only add $3_{6}$ .
$0_{6} +3_{6}$

STEP 9

Calculate the sum of the thousands place.
$_{6} +3_{6} =3_{6}$

STEP 10

Combine the sums of each place to get the final result in base6.
$3_{6}5_{6}3_{6}3_{6}$ The sum of $412_{6}$ and $312_{6}$ in base6 is $3533_{6}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCalculate the sum: 4126+31216412_{6}+3121_{6}4126​+31216​.

Studdy Solution

STEP 1

Assumptions1. The numbers are in base6 (denoted by the subscript6) . We are adding two numbers in base63. We need to convert the result to base6 if it exceeds5 (since base6 only has digits from0 to5)

STEP 2

Let's start by adding the numbers in the units place (rightmost digit).26+162_{6} +1_{6}26​+16​

STEP 3

Calculate the sum of the units place.26+16=362_{6} +1_{6} =3_{6}26​+16​=36​

STEP 4

Now, let's add the numbers in the tens place (second digit from the right).16+261_{6} +2_{6}16​+26​

STEP 5

Calculate the sum of the tens place.1+2=31_{} +2_{} =3_{}1​+2​=3​

STEP 6

Next, let's add the numbers in the hundreds place (third digit from the right).46+164_{6} +1_{6}46​+16​

STEP 7

Calculate the sum of the hundreds place.46+16=564_{6} +1_{6} =5_{6}46​+16​=56​

STEP 8

Finally, add the number in the thousands place (fourth digit from the right) to the sum. Since 4126412_{6}4126​ doesn't have a thousands place, we only add 363_{6}36​.06+360_{6} +3_{6}06​+36​

STEP 9

Calculate the sum of the thousands place.6+36=36_{6} +3_{6} =3_{6}6​+36​=36​

STEP 10

Combine the sums of each place to get the final result in base6.365636363_{6}5_{6}3_{6}3_{6}36​56​36​36​The sum of 4126412_{6}4126​ and 3126312_{6}3126​ in base6 is 353363533_{6}35336​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCalculate the sum: $412_{6}+3121_{6}$ .

Let's start by adding the numbers in the units place (rightmost digit).
$2_{6} +1_{6}$

Calculate the sum of the units place.
$2_{6} +1_{6} =3_{6}$

Now, let's add the numbers in the tens place (second digit from the right).
$1_{6} +2_{6}$

Calculate the sum of the tens place.
$1_{} +2_{} =3_{}$

Next, let's add the numbers in the hundreds place (third digit from the right).
$4_{6} +1_{6}$

Calculate the sum of the hundreds place.
$4_{6} +1_{6} =5_{6}$

Finally, add the number in the thousands place (fourth digit from the right) to the sum. Since $412_{6}$ doesn't have a thousands place, we only add $3_{6}$ .
$0_{6} +3_{6}$

Calculate the sum of the thousands place.
$_{6} +3_{6} =3_{6}$

Combine the sums of each place to get the final result in base6.
$3_{6}5_{6}3_{6}3_{6}$ The sum of $412_{6}$ and $312_{6}$ in base6 is $3533_{6}$ .