Steps to Convert a Negative Number to Hexadecimal:
Understand the Bit Width:
Decide the bit width (e.g., 8 bits, 16 bits, 32 bits, etc.). This determines how many bits are used to store the number in binary and affects the final hexadecimal result.
Convert the Positive Equivalent to Binary: Take the absolute value of the negative number and convert it to binary. For example, if the number is -10, the absolute value is 10, and its binary representation is 1010 (in 4 bits).
Pad the Binary Number: Pad the binary number with leading zeros to match the chosen bit width. For example, 1010 becomes 00001010 in an 8-bit representation.
Invert the Bits (One's Complement): Flip all the bits (0 becomes 1, and 1 becomes 0). For 00001010, the one's complement is 11110101.
Add 1 to the Inverted Binary Number (Two's Complement): Add 1 to the one's complement binary number to get the two's complement. For 11110101, adding 1 gives 11110110.
Group Binary Digits into Nibbles: Divide the binary number into groups of 4 bits (nibbles) starting from the right. For 11110110, the groups are 1111 and 0110.
Convert Each Nibble to Hexadecimal: Convert each group of 4 bits into its hexadecimal equivalent. For 1111, the hex is F, and for 0110, the hex is 6.
Combine the Hex Digits: Concatenate the hexadecimal digits to get the final result. For 11110110, the hexadecimal result is F6.
Below is an example:
Convert -10 to 8-bit hexadecimal:
Bit Width: 8 bits.
Positive Binary: ∣10∣=10 → 1010.
Pad to 8 Bits: 00001010.
Invert Bits: 11110101.
Add 1: 11110101 + 1 = 11110110.
Group into Nibbles: 1111 and 0110.
Convert to Hex: 1111 = F, 0110 = 6.
Final Hex: F6.