Binary Digits
 Decimal digits have 10 possible values ranging from 0 to 9
 Bits have only two possible values: 0 and 1.
 A binary number is composed of only 0s and 1s
The number 1001 has 4 digits located in 4 "positions"
1  0  0  1  <=====  Binary Digits 
3  2  1  0  <===== 
Position

1x23  0x22  0x21  1x20  <====  Equivalent Power of 2 
Step by step solution
Step 1: Write down the binary number: 1001 and note its digits in the 4 bits from right to left
Step 2: Multiply each digit of the binary number by the corresponding power of two:
1x2^{3} + 0x2^{2} + 0x2^{1 }+ 1x2^{0}
Step 3: Solve the powers:
1x8 + 0x4 + 0x2 + 1x1 = 8 + 0 + 0 + 1
Step 4: Add up the numbers written above:
8 + 0 + 0 + 1 = 9.
Solution: The number 9, therefore, is the decimal equivalent of the binary number 1001.
1  1  1  1  <=====  Binary Digits 
3  2  1  0  <=====  Position 
1  0  0  0  0  <=====  Binary Digits 
4  3  2  1  0  <=====  Position 
Step 1: Keep dividing (85)_{10} successively by 2, collect all the remainders until the quotient is 0:
85/2 = 42, remainder is 1... note here that 85/2 = 42 + 0.5; the remainder of the division is actually 0.5 but in these cases it is always rounded off to 1
42/2 = 21, remainder is 0
21/2 = 10, remainder is 1
10/2 = 5, remainder is 0
5/2 = 2, remainder is 1 ... note here again that 5/2 = 2 + 0.5; the remainder of the division is actually 0.5 but it was rounded off to 1
2/2 = 1, remainder is 0
1/2 = 0, remainder is 1 ... again the remainder was 0.5 but was rounded off to 1
Step 2: Read and collect all the binary digits from the bottom to the top as 1010101.
Therefore the binary number 1010101 is the binary equivalent of the decimal number 85