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.