Find the representation of the number 256 in the following bases:
a. base six
b. base twelve
c. base two
I get how to write the number of objects as a base(whatever), but I think this is asking me to start from the end number and work backwards. I really need help. I have two different questions concerning this math concept.
To find the number 286 in base 12, you divide 286 by 12, note the remainder, and keep dividing until the quotient is less than 12.
286/12 = 23 R 10
23/12 = 1 R 11
286 in base 12 would be 1(11)(10).
If we use the usual notation where A=10, B=11, we have
28610 = 1BA12
If you proceed the same way for other bases or numbers, you will get the right answers. Post your answers for checking if you wish.
i am working on a math project and i need 10 different representations of the number 256..its due tomorrow
To find the representation of the number 256 in different bases, you need to understand the concept of place value. In any base, including base six, base twelve, and base two, the position of a digit determines its value.
a. To convert 256 to base six, you start by dividing the number by 6. The remainder becomes the rightmost digit in the base six representation. Then, you divide the quotient by 6 again, and continue this process until the quotient becomes zero. Here's how it works:
256 ÷ 6 = 42 remainder 4
42 ÷ 6 = 7 remainder 0
7 ÷ 6 = 1 remainder 1
1 ÷ 6 = 0 remainder 1
Reading the remainders from bottom to top, we get the base six representation of 256 as 1044.
b. For base twelve, the process is similar. Here's how you can convert 256 to base twelve:
256 ÷ 12 = 21 remainder 4
21 ÷ 12 = 1 remainder 9
1 ÷ 12 = 0 remainder 1
Reading the remainders from bottom to top, the base twelve representation of 256 is 194.
c. To convert 256 to base two, also known as binary, you follow a similar approach:
256 ÷ 2 = 128 remainder 0
128 ÷ 2 = 64 remainder 0
64 ÷ 2 = 32 remainder 0
32 ÷ 2 = 16 remainder 0
16 ÷ 2 = 8 remainder 0
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top, the base two representation of 256 is 100000000.
In summary:
a. 256 in base six is represented as 1044.
b. 256 in base twelve is represented as 194.
c. 256 in base two (binary) is represented as 100000000.