Find the representation of the number 256 in thefollowing bases:a. Base six b. Base twelvec. Base two

a. Do it in decimal notation first.

256 = 216 + 36 + 4
= 1*6^3 + 1*6^2 + 0*6^1 + 4*6^0
That would be 1104 in base 6 notation

b. 256 = 1*12^2 + 9*12 + 4*12^0
That would be 194 in base 12 notation, which would should have letter symbols for 10 and 11, although we did not need them.

c. (binary)
256 = 1*2^8 +0*2^7 +0*2^6 +.. 0*2^0
= 100000000

To find the representation of a number in different bases, we need to perform a process called "base conversion". I will guide you through the steps to find the representations of the number 256 in base 6, base 12, and base 2.

a. Base 6:
To express 256 in base 6, we divide the number by 6 repeatedly until the quotient becomes zero. The remainders at each step will give us the representation in base 6.

256 ÷ 6 = 42 with a remainder of 4 (least significant digit)
42 ÷ 6 = 7 with a remainder of 0
7 ÷ 6 = 1 with a remainder of 1 (most significant digit)
1 ÷ 6 = 0 with a remainder of 1

The remainders, read from bottom to top, give us the representation of 256 in base 6. Therefore, 256 in base 6 is represented as 1144.

b. Base 12:
Similar to base 6, we will divide 256 by 12 repeatedly and keep track of the remainders to get the representation in base 12.

256 ÷ 12 = 21 with a remainder of 4 (least significant digit)
21 ÷ 12 = 1 with a remainder of 9
1 ÷ 12 = 0 with a remainder of 1 (most significant digit)

Reading the remainders from bottom to top, we obtain the representation of 256 in base 12. Thus, 256 in base 12 is represented as 194.

c. Base 2:
Converting a number to base 2 (binary) involves repeatedly dividing it by 2 and noting down the remainders.

256 ÷ 2 = 128 with a remainder of 0 (least significant digit)
128 ÷ 2 = 64 with a remainder of 0
64 ÷ 2 = 32 with a remainder of 0
32 ÷ 2 = 16 with a remainder of 0
16 ÷ 2 = 8 with a remainder of 0
8 ÷ 2 = 4 with a remainder of 0
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0 (most significant digit)
1 ÷ 2 = 0 with a remainder of 1

The remainders, read from bottom to top, give us the representation of 256 in base 2. Thus, 256 in base 2 is represented as 100000000.