Binary to decimal and decimal to binary

[2] Represent the following decimal
numbers in binary form using 0’s and 1’s
(base 2).
17, 24, 65, 217, 3

[3] Represent the following binary numbers
in decimal form (base 10).
1111, 1011, 1111111, 1101, 111000

To divide from decimal to binary, divide by 2 and note the remainder:

17 / 2 = 8 remainder 1
8 / 2 = 4 remainder 0
4 / 2 = 2 remainder 0
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1

Then write out the remainders in ascending order (i.e. the bottom remainder first) to get 10001

So 17 in decimal = 10001 in binary.

To convert from binary to decimal, you need to remember that each digit to the left has gone up by a power of 2, just like a decimal number goes up to the power of 10.

I.e. binary = 1, 2, 4, 8, 16, 32 etc.
Decimal = 10, 100, 1000 etc.

So for 1111, there's 1 in the 1s, 2s, 4s, and 8s column. 1 + 2 + 4 + 8 = 16
1111 = 16


Similarly 1101 = 1 + 4 + 8 = 13

256...128...64.....32.....16.....8......…
..0......0......0......0........1.....… = 17
..0......0......0......0........1.....… = 24
..0......0......1......0........0.....… 65
..0......1......1......0........1.....…
..0......0......0......0........0.....… = 3

15
11
127
13
56
as above