Final answer:
To convert -77 base 10 to 8-bit binary using signed magnitude notation, we take the binary of 77 (1001101), add an extra 0 to make it 8 bits (01001101), and then flip the leftmost bit for the negative sign (11001101).
Step-by-step explanation:
The conversion of -77 base 10 to 8-bit binary and to hex using signed magnitude notation starts with finding the binary representation of 77, which is 1001101. To fit this into 8 bits, we add a zero at the beginning: 01001101. Since the number is negative, the signed magnitude notation requires flipping the most significant bit (the leftmost bit) to 1, indicating a negative number. So the 8-bit binary representation of -77 is 11001101.
The hexadecimal representation can be found by converting the binary digits in pairs, from right to left. The binary 11001101 is grouped into pairs (11)(00)(11)(01), which translates to B (for binary 11), 0 (for binary 00), B (for binary 11), and 5 (for binary 01), resulting in the hex representation as B0B5. However, since we're working with signed magnitude, the most significant bit doesn't get translated into hexadecimal; its only purpose is to represent the sign (negative) of the number. Therefore, the correct representation would disregard the first binary digit when converting to hexadecimal, leaving us with 4D in hex.