QuestionCalculate $72_{8}+40$ .

Studdy Solution

STEP 1

Assumptions1. The first number is in base8 (octal) notation $72_{8}$ . The second number is in base10 (decimal) notation $40$
3. We need to add these two numbers together.

STEP 2

First, we need to convert the octal number to decimal. The formula to convert an octal number to decimal is $Decimal = d_{n} \times8^{n} + d_{n-1} \times8^{n-1} + \cdots + d_{0} \times8^{0}$ where $d_{n}$ is the digit at the nth position from the right (starting from0).

STEP 3

Now, plug in the given values for the digits of the octal number to calculate its decimal equivalent.
$Decimal =2 \times8^{0} +7 \times8^{1}$

STEP 4

Calculate the decimal equivalent of the octal number.
$Decimal =2 \times1 +7 \times8 =2 +56 =58$ So, $72_{8}$ is equal to $58$ in decimal notation.

STEP 5

Now that we have both numbers in decimal notation, we can add them together.
$Sum = Decimal_{1} + Decimal_{2}$

STEP 6

Plug in the values for the decimal equivalents of the octal number and the given decimal number to calculate the sum.
$Sum =58 +40$

STEP 7

Calculate the sum.
$Sum =58 +40 =98$ The sum of $72_{}$ and $40$ is $98$ .

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