Final answer:
To interpret the hexadecimal bit pattern 0xffd9 as a 16-bit 2's complement number, we need to convert it into binary representation and determine its value. The decimal value of 0xffd9 as a 16-bit 2's complement number is -39. If we reinterpret a negative integer n as an unsigned number, its numeric value as a function of n and k can be calculated by subtracting 2^k from the unsigned representation of n.
Step-by-step explanation:
To interpret the hexadecimal bit pattern 0xffd9 as a 16-bit 2's complement number, we need to convert it into binary representation and determine its value. The hexadecimal representation 0xffd9 is equivalent to the binary pattern 1111 1111 1101 1001. Since the leftmost bit is 1, it indicates a negative number.
In 2's complement representation, to find the decimal value of a negative number, we first invert all the bits (change 0s to 1s and 1s to 0s) and then add 1 to the result. In our case, the inverted binary pattern is 0000 0000 0010 0110. Adding 1 gives us 0000 0000 0010 0111. Therefore, the decimal value of 0xffd9 as a 16-bit 2's complement number is -39.
If we reinterpret a negative integer n as an unsigned number, its numeric value as a function of n and k can be calculated by subtracting 2^k from the unsigned representation of n. For example, if we have a negative integer -5 represented as a 4-bit 2's complement bit pattern (1011), its unsigned value can be found by subtracting 2^4 from the unsigned representation of 5, which is 0101. Thus, the numeric value of -5 as an unsigned 4-bit number is 5 - 2^4 = 5 - 16 = -11.