Hexadecimal to Binary Conversion Quiz

Hexadecimal digits represent values in base 16, where 'F' corresponds to the decimal value 15. In binary, 15 is represented as 1111, which consists of four bits. Each bit represents a power of 2, confirming that 'F' in hexadecimal translates to 1111 in binary.

To convert the hexadecimal number A to binary, we start by recognizing that A in hexadecimal represents the decimal value 10. In binary, the decimal number 10 is represented as 1010. Therefore, the binary equivalent of the hexadecimal A is 1010.

Hexadecimal digits represent values in base 16. The hex digit '3' corresponds to the decimal value 3. In binary, the decimal number 3 is represented as 0011, which uses four bits to show its value. Each bit represents a power of 2, confirming that 0011 accurately reflects the hex digit '3'.

Hexadecimal 1F represents 31 in decimal. To convert it to binary, each hex digit corresponds to a 4-bit binary representation. The digit '1' is 0001 and 'F' is 1111. Combining these gives 00011111, which is the binary representation of hex 1F.

Hexadecimal C represents the decimal value 12. In binary, 12 is expressed as 1100, where each digit corresponds to a power of 2: \(1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0\), which sums to 12. Thus, hex C is equivalent to the binary number 1100.

Hexadecimal 2A represents the decimal number 42. To convert it to binary, each hex digit is replaced with its 4-bit binary equivalent. The digit '2' translates to '0010' and 'A' (which is 10 in decimal) translates to '1010'. Combining these gives the binary representation: 00101010.

The hexadecimal system is base 16, where each digit represents a value from 0 to 15. The digit '7' in hexadecimal corresponds directly to the decimal value 7. In binary, the decimal number 7 is represented as 0111, using four bits to accurately reflect its value in a binary format.

Hexadecimal 5E converts to binary by translating each hex digit into its 4-bit binary equivalent. The hex digit '5' is represented as 0101 and 'E' as 1110. Combining these gives 01011110, which is the binary representation of hex 5E.

Hexadecimal B corresponds to the decimal value 11. In binary, 11 is represented as 1011. Each hex digit converts to a 4-bit binary equivalent, and since B is the only digit here, it directly translates to 1011 in binary format.

Hexadecimal 9D converts to binary by translating each hex digit into its 4-bit binary equivalent. The digit '9' in hex is '1001' in binary, and 'D' (which equals 13 in decimal) is '1101' in binary. Combining these gives the full binary representation: 10011101.

Hexadecimal 4 is represented in binary as 0100. Each hex digit corresponds to a 4-bit binary value, and since 4 in decimal is 4 in hex, its binary representation is straightforwardly 0100, where the leading zeros are included to maintain the 4-bit format.

Hexadecimal FF represents the decimal value 255. In binary, this value is expressed as 11111111, which consists of eight bits, all set to 1. Each hex digit corresponds to four binary digits, and FF translates directly to the maximum value for an 8-bit binary number.