With binary we need a method of representing negative numbers. The simplest way to do this (though not the best) is to use the sign and magnitude method.
In sign and magnitude binary, a number is expressed using a combination of a sign bit and a magnitude (the absolute value of the number). They combine together to make the full signed number.
The sign bit indicates positive (0) or negative (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 (11001)
What is the advantage of sign and magnitude representation?
In sign and magnitude representation, the leftmost bit represents the sign. What value represents a positive number?
In sign and magnitude representation, the binary number 10011011 represents the decimal number .
What happens if both the leftmost bit and the remaining bits are zero in sign and magnitude representation?
Issues with Sign and Magnitude
Sign and Magnitude has two key issues:
Issue 1: Two Representations of Zero
In sign and magnitude representation, there are two representations of zero - one positive (all bits set to 0) and one negative (sign bit set to 1, all other bits set to 0). This can cause confusion and lead to errors in calculations and comparisons.
For example 0000 = 0 ; 1000 = 0
Issue 2: Difficulty in Performing Arithmetic Operations
Performing arithmetic operations, such as addition and subtraction, on sign and magnitude numbers can be complex. Additional logic is required to handle the signs, which makes the operations more difficult and processor intensive to implement using digital circuitry
Using sign and binary the number 20 is represented as .
What is the disadvantage of sign and magnitude representation?
In sign and magnitude binary, there are representations for zero.
