Converting Positive Decimal to Binary with Enthusiasm!

Are you ready to convert positive decimal numbers to binary with me?

Let's have some fun converting the following decimal numbers into binary!

1. Convert decimal 15 into 8-bit binary.

2. Convert decimal 8 into 8-bit binary.

3. Convert decimal 65 into 8-bit binary (use the hint: 64 = 2^6).

4. Convert decimal 31 into 8-bit binary (use the hint: 32 = 2^5).

5. Convert decimal 2063 into 16-bit binary (use the hint: 2048 = 2^11 and also, 2063= 2048 + 15).

Let's Dive into the Wonderful World of Binary Conversion!

Are you curious to learn how to convert positive decimal numbers into binary representation?

Stay tuned as we break down the conversion process step by step for each decimal number!

In Mathematics, we can convert positive decimal numbers to binary using the powers of 2. The 8-bit binary representations for 15, 8, 65, and 31 are 0000 1111, 0000 1000, 0100 0001, and 0001 1111, respectively. The 16-bit binary equivalent for 2063 is 0111 1111 1111.

Explanation: In Mathematics, we often convert different codes from one type to another. When converting positive decimal numbers to binary, start by finding the largest power of 2 that fits into the number, and represent that as a 1 in the corresponding place value. Remainders then convert as smaller powers of 2, down to 2^0 = 1.

Let's tackle your questions:

- 15 is equal to 2^3 + 2^2 + 2^1 + 2^0. Therefore, 15 is represented as 0000 1111 in 8-bit binary format.

- 8 in binary is 2^3, so in 8-bit binary, it's represented as 0000 1000.

- To convert 65 (2^6 + 2^0) into 8-bit binary, represent it as 0100 0001.

- 31 can be represented as 2^4 + 2^3 + 2^2 + 2^1 + 2^0, thus 31 in binary is 0001 1111.

- For 2063 (2^11 + 2^3 + 2^2 + 2^1 + 2^0), in binary we obtain 0111 1111 1111.