Question - Base 7 Subtraction Calculation
Solution:
The question asks to determine the difference between 6442 in base 7 and 5603 in base 7. To perform the subtraction, we need to subtract each digit, starting from the rightmost and moving to the left. If a digit in the subtrahend is larger than the digit in the minuend, we need to borrow from the next left digit in the minuend.Starting from the ones place:2 (base 7) - 3 (base 7) cannot be done directly because 2 is less than 3, so we borrow from the next digit.12 (base 7) - 3 (base 7) = 6Moving to the tens place, since we have borrowed 1 from it:3 (base 7) becomes 2 (base 7) now.4 (base 7) - 0 (base 7) remains as is, since there's nothing to subtract.2 (base 7) - 2 (base 7) = 0Next, the hundreds place:4 (base 7) - 6 (base 7) cannot be done directly, so we borrow from the next digit.14 (base 7) - 6 (base 7) = 8 (since when we borrow in base 7, we're borrowing a group of 7, 7 + 4 = 11, but we're in base 7, so it reads as 14).For the thousands place:6 (base 7) becomes 5 (base 7) because we just borrowed 1.5 (base 7) - 5 (base 7) = 0Write down the digits we've calculated from right to left to find the answer:(0)8076 (base 7)Therefore, the difference is 8076 in base 7.
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