Add 777 + 605 to base 8
777 + 605 in base 8 is 1424.
To add 777 and 605 in base 8, follow these steps:
Step 1: Convert the numbers to base 10.
777 (base 8) = 511 (base 10)
605 (base 8) = 397 (base 10)
Step 2: Add the converted numbers in base 10.
511 + 397 = 908
Step 3: Convert the result back to base 8.
908 (base 10) = 1604 (base 8)
So, 777 (base 8) + 605 (base 8) = 1604 (base 8).
To add the numbers 777 + 605 in base 8, we first need to convert the numbers to base 10 and then perform the addition. After that, we can convert the result back to base 8.
To convert 777 and 605 from base 8 to base 10:
1. Take each digit of the number multiplied by 8 to the power of its position (starting from the rightmost digit).
2. Add up all the products from step 1 to get the decimal value.
For 777:
7 * 8^2 + 7 * 8^1 + 7 * 8^0 = 7 * 64 + 7 * 8 + 7 = 448 + 56 + 7 = 511
For 605:
6 * 8^2 + 0 * 8^1 + 5 * 8^0 = 6 * 64 + 0 * 8 + 5 = 384 + 5 = 389
Now we can add the base 10 numbers together:
511 + 389 = 900
The sum of 777 + 605 in base 10 is 900.
To convert the result 900 back to base 8:
1. Divide the number repeatedly by 8 until the quotient becomes 0.
2. The remainders at each step from the last remainder forms the base 8 representation of the number.
Dividing 900 by 8 repeatedly:
900 ÷ 8 = 112 with a remainder of 4 (first remainder)
112 ÷ 8 = 14 with a remainder of 0 (second remainder)
14 ÷ 8 = 1 with a remainder of 6 (third remainder)
1 ÷ 8 = 0 with a remainder of 1 (fourth remainder)
The remainders (in reverse order) give us the base 8 representation which is 1460.
Therefore, the sum of 777 + 605 in base 8 is 1460.