Match the decimal numbers on the left with their binary representations on the right.

Decimal to Binary Conversion

• 16 in decimal is 10000 in binary.
• 10 in decimal is 1010 in binary.
• 20 in decimal is 10100 in binary.
• 21 in decimal is 10101 in binary.
• 8 in decimal is 1000 in binary.
• 111 in decimal is 1101111 in binary.

Explanation:

Binary representation uses powers of 2. Each digit's place value in binary is a power of 2, starting from 2^0 on the rightmost side. To convert a decimal number to binary, you find the largest power of 2 that fits into the decimal number, subtract it, and repeat the process with the remainder until you reach zero. For example, to convert 10 to binary: The largest power of 2 less than or equal to 10 is 8 (2^3). So, we have a 1 in the 2^3 place. The remainder is 10 - 8 = 2. The largest power of 2 less than or equal to 2 is 2 (2^1). So, we have a 1 in the 2^1 place. The remainder is 2 - 2 = 0. We have 0s in the places for 2^2 and 2^0. Therefore, 10 in decimal is 1010 in binary.