Signed magnitude representation
Summary
Detail
The concept behind SMR is similar to how we designate positive and negative integers in denary mathematics: we use a dedicated symbol (-) to signpost that the integer is negative. In the binary application the dedicated symbol is one of the binary digits that comprise the number.
Typically 0 is used to indicate an unsigned (positive) integer and 1 to indicate a signed (negative) number. The rest of the bits are the magnitude (the actual numerical value).
We can demonstrate with an 8-bit binary system, encoding 5: 0000 0101. Here the furthest bit (aka. the “most significant bit” (MSB)) at the \(2^8\) position is 0, designating that the number is unsigned. The signed equivalent is 1000 0101, with the MSB being 1 designating the number as signed. When we are working with signed numbers, the MSB is known as the signed bit.
