Convert the base 10 number in the indicated base. 40 to base 2
I get so confused on how to do this.
Converting a base 10 number to another base, such as base 2, can be done by using a process called "division by base."
To convert a base 10 number to base 2, follow these steps:
1. Start by dividing the number (40 in this case) by 2.
Divide 40 ÷ 2 = 20 with a remainder of 0.
2. Write down the remainder (0) as the rightmost digit in the new base (base 2).
So far, the converted number is 0.
3. Next, divide the quotient (20) from step 1 by 2.
Divide 20 ÷ 2 = 10 with a remainder of 0.
4. Again, write down the remainder (0) as the next digit to the left of the previous one.
The converted number is still 0.
5. Repeat the division process with the new quotient (10) until the quotient becomes 0.
Divide 10 ÷ 2 = 5 with a remainder of 0.
Divide 5 ÷ 2 = 2 with a remainder of 1.
Divide 2 ÷ 2 = 1 with a remainder of 0.
6. For the last division when the quotient becomes 1, write down the remainder (1) as the next digit to the left.
The converted number is now 010 (reading from right to left).
7. When the quotient is 1, the process is complete, and the remaining quotient (1) should be added as the leftmost digit.
The final converted number is 1010, which is the base 2 representation of the base 10 number 40.
So, 40 in base 10 is equal to 1010 in base 2.