The Decimal Representation of 1001 1001 (Base 2) in Two's Complement

What is the decimal representation of 1001 1001 (base 2) in two's (2's) complement?

The decimal representation of 1001 1001 (base 2) in two's (2's) complement is -103 (base 10).

Understanding Two's Complement

In two's complement, the leftmost bit of a binary number represents the sign, where 1 indicates a negative number and 0 indicates a positive number. The process of converting a binary number to its decimal equivalent in two's complement involves interpreting the leftmost bit as a sign bit and then calculating the magnitude of the number. When we have the binary number 1001 1001 in two's complement, the leftmost bit is 1, indicating a negative number. To convert this binary number to decimal, we first take the complement of the remaining bits (001 0111) and then add 1 to the result. Taking the complement of 001 0111 gives us 110 1001. Adding 1 to this result, we get the decimal representation of -103. Therefore, the decimal representation of the binary number 1001 1001 in two's complement is -103 in base 10. This process is crucial in understanding how negative numbers are represented in binary form using two's complement.
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