Final answer:
The binary expansion of 21 is expressed as the sum of powers of 2: 21 = 2^4 + 2^2 + 2^0, which converts to the binary notation 10101.
Step-by-step explanation:
To complete the binary expansion of 21, we need to express the number 21 as the sum of powers of 2. Starting from the highest power of 2 that is less than 21, we get:
- 21 = 16 + 5
- 16 = 24
- 5 = 4 + 1
- 4 = 22
- 1 = 20
Therefore, the binary expansion of 21 is given by:
21 = 24 + 22 + 20
In binary notation, this is written as 10101, where each digit represents a power of 2 that is present in the expansion.