Questions: Question 5 Perform the indicated operation. 34eight+61eight 105eight None of these 106eight 115eight

Transcript text: Question 5 Perform the indicated operation. \[ 34_{\text {eight }}+61_{\text {eight }} \] $105_{\text {eight }}$ None of these $106_{\text {eight }}$ $115_{\text {eight }}$

Solution

Solution Steps

To solve the problem of adding two numbers in base eight (octal), we first convert the octal numbers to decimal (base ten), perform the addition in decimal, and then convert the result back to octal.

Step 1: Convert Octal to Decimal

We start by converting the octal numbers $34_{\text{oct}} $ and $61_{\text{oct}} $ to decimal (base ten).

\[ 34_{\text{oct}} = 3 \times 8^1 + 4 \times 8^0 = 24 + 4 = 28 \]

\[ 61_{\text{oct}} = 6 \times 8^1 + 1 \times 8^0 = 48 + 1 = 49 \]

Step 2: Perform Addition in Decimal

Next, we add the two decimal values obtained:

\[ 28 + 49 = 77 \]

Step 3: Convert the Result Back to Octal

Now, we convert the sum $77$ back to octal:

\[ 77_{\text{dec}} = 115_{\text{oct}} \]