Arithmetic Operations in Different Bases

The video tutorial covers the addition and subtraction of numbers in various bases, including base 2, base 4, base 6, base 7, and base 8. It provides step-by-step examples for each base, explaining how to handle values that exceed the base by dividing and carrying over remainders. The tutorial also includes a practical example of calculating the perimeter of a rectangle using base 2 arithmetic. The video emphasizes understanding the borrowing and carrying process in different bases, which is similar to the decimal system but adjusted for the specific base.

What is the key difference when adding numbers in bases other than 10?

• The rules of addition change completely.

• You use base 10 for all calculations.

• You borrow or carry over the base value instead of 10.

• You cannot perform addition in other bases.

In base 2, what do you do when the sum of two digits equals 2?

• Write 2 and carry over 0.

• Write 0 and carry over 2.

• Write 0 and carry over 1.

• Write 1 and carry over 0.

What is the result of adding 1101 and 1110 in base 2?

• 10111

• 10101

• 11001

• 11011

In base 8, what happens when the sum of two digits is 8?

• Write 8 and carry over 0.

• Write 0 and carry over 1.

• Write 1 and carry over 0.

• Write 0 and carry over 8.

What is the sum of 345 and 453 in base 8?

• 1100

• 1010

• 1000

• 1020

In base 7, what do you do when the sum of two digits is 7?

• Write 0 and carry over 7.

• Write 1 and carry over 0.

• Write 0 and carry over 1.

• Write 7 and carry over 0.

What is the result of adding 456 and 321 in base 7?

• 1000

• 1100

• 1020

• 1010

In base 4, what do you do when the minuend is smaller than the subtrahend?

• Borrow 4 from the next digit.

• Borrow 10 from the next digit.

• Subtract directly without borrowing.

• Borrow 1 from the next digit.

What is the result of subtracting 132 from 321 in base 4?

• 123

• 312

• 231

• 213

In base 2, what do you do when the minuend is smaller than the subtrahend?

• Borrow 1 from the next digit.

• Borrow 10 from the next digit.

• Borrow 2 from the next digit.

• Subtract directly without borrowing.