With binary we need a method of representing numbers. The simplest way to do this (though not the best) is to use the and magnitude method. In sign and magnitude binary, a number is expressed using a combination of a and a (the absolute value of the number). They combine together to make the full signed number. The sign bit indicates positive (0) or (1) and the rest of the number is just a normal binary number.
In the example above, the number -25 is represented by the sign bit (1) and the absolute value (). Sign and Magnitude has two key issues: the first issue is that there are two representations of zero - one positive (all bits set to 0) and one (sign bit set to 1, all other bits set to 0). This can cause confusion and lead to in calculations and comparisons. For example, 0000 = 0 ; 1000 = 0.
The second issue is the difficulty in performing arithmetic operations, such as and subtraction, on sign and magnitude numbers. Performing these operations can be complex. Additional is required to handle the signs, which makes the operations more difficult and processor intensive to implement using digital circuitry.
