Final answer:
In two's complement representation, an 8-bit number beginning with a 1 denotes a negative value, and one beginning with a 0 denotes a positive value. For 11010011, the corresponding decimal sign-and-magnitude value is -45, and for 01000011, it is +67.
Step-by-step explanation:
The two's complement system is a method used in computing to represent positive and negative integers. To decode an 8-bit two's complement number to its decimal sign-and-magnitude value, we look at the most significant bit (MSB) to determine the sign. If the MSB is 1, the number is negative; if it's 0, the number is positive. To find the magnitude, if the number is negative, we invert all the bits and add 1 to the result.
a) The 8-bit number 11010011 in two's complement represents a negative number because the MSB is 1. Inverting the bits gives 00101100, and adding 1 gives 00101101, which is 45 in decimal. Therefore, the sign-and-magnitude value is -45.
b) The 8-bit number 01000011 in two's complement has an MSB of 0, so it's a positive number. The magnitude is the same as the binary value, which is 67 in decimal. Therefore, the sign-and-magnitude value is +67.
The mention correct option in the final answer is that the decimal sign-and-magnitude values for the 8-bit two's complement numbers 11010011 and 01000011 are -45 and +67, respectively.