Binary Negative Numbers

Although we have covered in detail, the way the binary numbering system works, and how it relates to decimal and hexadecimal values, there is one area that has been omitted  .  .  .  negative numbers.  

Initially, the MSB (Most significant but) of a byte was used to signify positive or negative.  This meant that only 7 bits were left over to represent the number, and therefore, instead of a range of 0 to 255, the new range was -127 to +127.  Either way, the byte can represent a total of 255 different values.

But since today's computers yse 32-bit words - they now can use a signed bit to signify positive or negative, and still have plenty left over for the numeric portion.

PC numeric computations go into the billions, and they had to come up with techniques to work with these values.  They use exponential techniques, and multiple bytes strung together.  Unfortunately, this area is so complex, that it is beyond the scope of this website.