The binary number 1010₂ is computed as (1×2³) + (0×2²) + (1×2¹) + (0×2❰), which equals 8 + 0 + 2 + 0 = 10. Therefore, 10 is the correct answer.

15 in decimal converts to binary by summing the powers of 2: 8+4+2+1, which gives 1111₂. Thus, 1111 is the correct binary representation.

The binary number 1101₂ converts to decimal by calculating 1×2³ + 1×2² + 0×2¹ + 1×2❰, which equals 8 + 4 + 0 + 1 = 13. Therefore, 13 is the correct answer.

The number 7 in decimal is represented as 111 in binary since 4 + 2 + 1 equals 7. This makes 111 the correct conversion from decimal to binary.

A valid binary number contains only the digits 0 and 1. Among the options provided, only 101101 meets this criterion, making it the valid binary number.

To convert 23 in base 8 to decimal, multiply the first digit by 8 and add the second digit: 2×8 + 3 = 16+3 = 19. Thus, the correct answer is 19.

When 37 is converted to base 6, it is broken down into 1×6² + 0×6¹ + 1, which is written as 101. Therefore, 101 is the correct base 6 representation.

In base 3, 101 is calculated as 1×3² + 0×3¹ + 1×3❰, which equals 9 + 0 + 1 = 10. Hence, the correct answer is 10.

In base 5, only the digits 0 through 4 are valid. The number 34 uses only these digits, making it the proper representation in base 5.

For the number 27 in base 9, the conversion is computed as 2×9 + 7 = 18 + 7, which equals 25. Therefore, the correct decimal conversion is 25.

Dividing 50 by 16 gives a quotient of 3 with a remainder of 2, which in hexadecimal is written as 32 (3×16 + 2 = 50). Thus, 32 is the correct representation.

To convert 11001₂ to decimal, calculate 1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 16 + 8 + 0 + 0 + 1 = 25. Therefore, the correct answer is 25.

In hexadecimal, the letter A represents 10. Therefore, 1A₝₆ is calculated as 1×16 + 10 = 26. This confirms that 26 is the correct decimal equivalent.

For 201 in base 3, calculate 2×3² + 0×3¹ + 1×3❰ = 18 + 0 + 1, which equals 19. Thus, the correct answer is 19.

Converting 100 to binary through successive division by 2 results in 1100100₂. This confirms that 1100100 is the correct representation.

By grouping the binary digits into nibbles (0010 1101), we obtain the hexadecimal digits 2 and D respectively. Therefore, 2D is the correct hexadecimal conversion.

Each hexadecimal digit converts to a four-bit binary sequence. The digit 2 becomes 0010 and B (which stands for 11) becomes 1011; when combined (and dropping insignificant leading zeros) the result is 101011.

The binary fraction 10.101₂ is split into an integer part of '10' (which equals 2) and a fractional part '.101'. The fraction equals 0.5 + 0 + 0.125 = 0.625, and adding these gives 2.625.

Dividing 255 by 16 produces a quotient of 15 and a remainder of 15. Since 15 is represented by 'F' in hexadecimal, 255 converts to FF.

Expressing 121 in an unknown base (b) as 1×b² + 2×b + 1 gives (b+1)². Since (b+1)² = 16, we find that b+1 = 4, so b = 3. Therefore, the correct base is 3.