Question

Convert 22 to a numeral in base 2.

Answer 1

The answer is 10110

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Explanation:

Divide 22 over 2. Use long division to find the quotient and remainder
22/2 = 11 remainder 0 <<--- this remainder will be used later. Call it A, so A = 0

Now repeat for the value 11, which was the quotient above
11/2 = 5 remainder 1 <<--- this remainder will be used later. Call it B, so B = 1

Repeat again for the quotient we just got
5/2 = 2 remainder 1 <<--- this remainder will be used later. Call it C, so C = 1

Repeat again
2/2 = 1 remainder 0 <<--- this remainder will be used later. Call it D, so D = 0

Repeat again
1/2 = 0 remainder 1 <<--- this remainder will be used later. Call it E, so E = 1

The last quotient above is 0, so we stop here. If we tried to keep going, then we'd get nothing but 0 remainders forever.

The remainders we got above were:
A = 0
B = 1
C = 1
D = 0
E = 1

The idea is to read the remainders in reverse order in which we found. So we start with E and work back to A
E = 1
D = 0
C = 1
B = 1
A = 0

So 22 base 10 = 10110 base 2

Answer 2

Base 2 is also known as binary.  We are going to use the division by 2 method.  We will divide the number by 2 and put the whole number in one section, and the remainder in another section, and when we get our whole number down to a 0 with a remainder of 1, then we are done.  22/2 gives us a whole number of 11 with a remainder of 0.  Divide 11/2 and we get a whole number of 5 with a remainder of 1.  Divide 5/2 and we get a whole number of 2 with a remainder of 1.  Divide 2/2 and get a whole number of 1 with a remainder of 0.  Divide 1/2 and get a whole number of 0 with a remainder of 1.  Working from the bottom to the top in the remainder section we have, in order, 10110.  That means that $22 _{10} =10110 _{2}$.  And that's it!