Can someone help me understand how to convert numbers to base numbers. Such as....
1. 40 to base two
2. 502 to base eight
3. 42 to base five
I have researched the web and cannot find a site that explains it in normal english! Any help would be appreciated.
I'd be happy to help you understand how to convert numbers to different base numbers! Converting numbers to different bases involves dividing the given number by the desired base repeatedly until the quotient becomes zero. During this process, the remainders obtained at each step are collected in reverse order to form the converted number.
Let's go through each example step-by-step:
1. Converting 40 to base two:
- Start by dividing 40 by 2: 40 ÷ 2 = 20 with a remainder of 0.
- Next, divide 20 by 2: 20 ÷ 2 = 10 with a remainder of 0.
- Divide 10 by 2: 10 ÷ 2 = 5 with a remainder of 0.
- Finally, divide 5 by 2: 5 ÷ 2 = 2 with a remainder of 1.
- The last quotient obtained is 2, which cannot be divided further, so we collect the remainders in reverse order: 101000. Therefore, 40 in base 10 is equivalent to 101000 in base 2.
2. Converting 502 to base eight:
- Begin by dividing 502 by 8: 502 ÷ 8 = 62 with a remainder of 6.
- Next, divide 62 by 8: 62 ÷ 8 = 7 with a remainder of 6.
- Finally, divide 7 by 8: 7 ÷ 8 = 0 with a remainder of 7.
- Collect the remainders in reverse order: 766. Thus, 502 in base 10 is equivalent to 766 in base 8.
3. Converting 42 to base five:
- Start by dividing 42 by 5: 42 ÷ 5 = 8 with a remainder of 2.
- Divide 8 by 5: 8 ÷ 5 = 1 with a remainder of 3.
- Finally, divide 1 by 5: 1 ÷ 5 = 0 with a remainder of 1.
- Collect the remainders in reverse order: 132. Therefore, 42 in base 10 is equivalent to 132 in base 5.
I hope this explanation helps you understand how to convert numbers to different base numbers!