Can you please help me with the arithmetic of binary numbers in fixed-point format.
I have two sign-magnitude 8-bit numbers, for example, 0_0101010 and 1_0001100, where the most significant bit represents the sign, and there is no integer part, meaning 7 bits are allocated for the fractional part. When multiplied, according to all rules, I get a 16-bit result, with 14 bits in the fractional part and two numbers to the left of the decimal point. How do I interpret these two numbers? Are they two sign bits? But in the case of 1_0000000 * 1_0000000 = 01_0000000_0000000, they are different. By the way, this is the only case when they are different. As I understand it, the sign bit is indeed the last one, i.e., the 16th bit, but how do I interpret the 15th bit?