Negative numbers are essential, and any computer not capable of dealing with them would not be particularly useful.  But how can such numbers be represented?  There are several methods which can be used to represent negative numbers in Binary.  One of them is called the Sign-Magnitude Method.

The Sign-Magnetude Method is quite easy to understand.  In fact, it is simply an ordinary binary number with one extra digit placed in front to represent the sign.  If this extra digit is a '1', it means that the rest of the digits represent a negative number.  However if the same set of digits are used but the extra digit is a '0', it means that the number is a positive one.  The following examples explain the Sign-Magnitude method better.

Let us assume that we have an 8-bit register.  This means that we have 7 bits which represent a number and the other bit to represent the sign of the number (the Sign Bit).
This is how numbers are represented:

The red digit means that the number is positive.  The rest of the digits represent 37.  Thus,
the above number in sign-magnitude representation, means +37.
And this is how -37 is represented:




Answer these questions:

1.  Write '-93' in sign-magnitude representation, using an 8-bit register. 
2. What is the largest positive number which can be represented in an 8-bit register, using the sign-magnitude method of representation? 
3.  What is the largest negative number which can be represented in an 8-bit register, using the sign-magnitude method of representation? 
4.  Give the range of possible numbers which can be represented in a 16-bit register, using the sign-magnitude method. From  to 

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Answers to above Activities

(1) 11011101
(2) +127 (01111111)
(3) -127 (11111111)
(4) from +32767 to -32767

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