Number bases

Question 1

What are the steps to add numbers in a different base?

Answer 1

1. Align the numbers by their least significant digits (rightmost digits).
2. Add digits starting from the rightmost column.
3. Carry over to the next column if the sum exceeds the base.
4. Repeat for each column until you reach the leftmost digits.

Question 2

What are the steps to subtract numbers in a different base?

Answer 2

1. Align the numbers by their least significant digits.
2. Subtract digits starting from the rightmost column.
3. Borrow from the next column if needed.
4. Repeat for each column until you finish.

Question 3

How do you multiply numbers in a different base?

Answer 3

1. Multiply each digit of the second number by each digit of the first number.
2. Write down partial products, shifted according to their position.
3. Add the partial products using the addition method in that base.

Question 4

How do you divide numbers in a different base?

Answer 4

1. Divide the digits of the dividend by the divisor, starting from the left.
2. Write down the quotient for each step.
3. Subtract the product of the divisor and the current quotient from the dividend.
4. Bring down the next digit and repeat until done.

Question 5

What are the steps to convert a number from one base to another?

Answer 5

1. Convert to Base 10: Multiply each digit by the base raised to the power of its position, then sum all these products.
2. Convert from Base 10: Divide the base 10 number by the new base, record the remainder, repeat with the quotient until it’s zero, and read the remainders in reverse order.

Question 5

How do you convert fractional parts from one base to another?

Answer 5

1. Convert the whole number part as usual.
2. Multiply the fractional part by the new base.
3. Record the integer part and use the fractional part for the next multiplication.
4. Repeat until the fraction is zero or reaches a repeating pattern.