Octal Subtraction and Borrow Operations Quiz

To subtract 7₈ from 15₈ in octal, first convert both numbers to decimal: 15₈ is 13 in decimal, and 7₈ is 7 in decimal. Subtracting gives 13 - 7 = 6 in decimal. Converting 6 back to octal results in 6₈, which is the final answer.

To subtract 23₈ from 15₈ in octal, first align the numbers: 23₈ - 15₈. Starting from the right, 3 - 5 requires borrowing, making it 13₈ - 5 = 6₈. Then, 2 - 1 yields 1. Thus, the result is 10₈, which is equivalent to 8 in decimal, confirming the answer as 8₈.

In octal subtraction, the base is 8, which means each digit can range from 0 to 7. When borrowing, you take from the next higher place value, similar to how you would in decimal (base 10), but in this case, you are working within the constraints of base 8.

To subtract 32₈ and 17₈ in octal, align the numbers and perform the subtraction as you would in decimal, borrowing as necessary. Starting from the right, 2 - 7 requires borrowing, turning the left digit into 2. After calculation, the result is 15₈, which is equivalent to 13 in decimal.

In octal (base 8) subtraction, borrowing 1 from the next column effectively adds 8 to the current column's value. This is because each column represents a power of 8, so borrowing 1 translates to 8 in the current column, allowing for proper subtraction within the constraints of octal arithmetic.

To subtract 50₈ and 23₈ in octal, align the numbers and subtract each digit starting from the right. In octal, 0 - 3 requires borrowing, making it 8 - 3 = 5. The next column becomes 4 - 2 = 2. Thus, the result is 25₈.

When subtracting 6₈ from 14₈, you compare the digits in each place value. The digit in the 8s place of 14 is 4, which is less than 6. Therefore, you need to borrow from the next higher place value to perform the subtraction correctly, confirming that borrowing is necessary.

To subtract octal numbers, align them by place value and subtract each digit while borrowing if necessary. For 77₈ - 35₈, subtract starting from the rightmost digit: 7 - 5 = 2, and then 7 - 3 = 4. Thus, the result is 42₈.

In octal subtraction, borrowing occurs when a digit in the minuend (the number from which another number is subtracted) is smaller than the corresponding digit in the subtrahend (the number being subtracted). When borrowing, the next left column decreases by 1, as octal is base 8, meaning each column represents powers of 8.

To subtract 102₈ and 45₈ in octal, align the numbers and subtract digit by digit, borrowing as needed. Starting from the rightmost digit, 2 (octal) minus 5 (octal) requires borrowing, making it 12₈ - 5₈ = 5₈. Next, 0 (after borrowing) minus 4 is 4, and finally, 1 minus nothing is 1. This gives 57₈.

In base 8 subtraction, borrowing is necessary when the digit in the minuend (top number) is smaller than the digit in the subtrahend (bottom number). In this case, 4 in the eights column is less than 7, requiring borrowing to perform the subtraction correctly.

To subtract the octal numbers 120₈ and 57₈, convert them to decimal: 120₈ is 80 and 57₈ is 47. Subtracting these gives 33 in decimal. Converting 33 back to octal results in 41₈. However, re-evaluating the subtraction in octal directly yields 43₈, confirming the correct answer.