How do you convert the decimal number 75 to binary?

The decimal number 75 converted to binary is 1001011.

Here's how you can convert decimal 75 to binary:

Method: Repeated Division by 2

1. Divide 75 by 2: 75 ÷ 2 = 37 with a remainder of 1.
2. Divide 37 by 2: 37 ÷ 2 = 18 with a remainder of 1.
3. Divide 18 by 2: 18 ÷ 2 = 9 with a remainder of 0.
4. Divide 9 by 2: 9 ÷ 2 = 4 with a remainder of 1.
5. Divide 4 by 2: 4 ÷ 2 = 2 with a remainder of 0.
6. Divide 2 by 2: 2 ÷ 2 = 1 with a remainder of 0.
7. Divide 1 by 2: 1 ÷ 2 = 0 with a remainder of 1.

Now, read the remainders from bottom to top: 1001011.

Therefore, the binary representation of the decimal number 75 is 1001011. This representation utilizes 7 bits (binary digits). In the binary system, each digit represents a power of 2, starting from the rightmost digit as 2⁰, then 2¹, 2², and so on. In this case:

(1 x 2⁶) + (0 x 2⁵) + (0 x 2⁴) + (1 x 2³) + (0 x 2²) + (1 x 2¹) + (1 x 2⁰) = 64 + 0 + 0 + 8 + 0 + 2 + 1 = 75