Книга: Introduction to Microprocessors and Microcontrollers

Signed magnitude numbers

The first attempt seemed easy but it was false optimism. All we had to do was to use the first bit (msb) of the number to indicate the sign 1 = minus, 0 = plus.

This had two drawbacks.

1 It used up one of the bits so an 8-bit word could now only hold seven bits to represent numbers and one bit to say ‘plus’ or ‘minus’. The seven bits can now only count up to 1111111₂=127 whereas the eight bits should count to 255.

2 If we added two binary numbers like +127 and +2, we would get:

The msb (most significant bit) of 1 means it is a minus number and the actual number is 0000001=1. So the final result of +127+2 is not 129 but minus 1.

When we use a microprocessor to handle arithmetic with these problems, we can ensure that the microprocessor can recognize this type of accidental negative number. We can arrange for the microprocessor to compensate for it but it is rather complicated and slow.

Luckily, a better system came along which has stood the test of time, having been used for many years.

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