1. An integer is a whole number, positive or negative. Every integer stored in the computer is allocated the same amount of space, whether it is a large integer or a small integer. The number of bits allocated determines the range of numbers which can be stored. If one byte was allowed then the largest integer would be: 11111111 which is 255 in decimal or 28 - 1 Two bytes would allow: 216 -1 possibilities = a range from 0 to 65535. Integers

2. If a computer only had to store positive integers then we could easily convert each number into its binary equivalent as you saw in the examples earlier. However, negative numbers have to be stored too and we need to find a method of representing a –ve sign using 1s and 0s. Modern computers use the Two’s complement method to represent integers. Negative Integers

3. With this method we take the most significant bit (the one on the far left) and treat it as a negative number . The following examples illustrate the principle using 4 bit numbers to help you understand. A modern computer would use 32 bit numbers for integers. In your NABS and final exams you are likely to be asked to use 8 bit number. Two's Complement

4. Binary Decimal 1000 -8 1001 -7 1010 -6 1011 -5 1100 -4 1101 -3 1110 -2 1111 -1 0000 0 0001 +1 0010 +2 0011 +3 0100 +4 0101 +5 0110 +6 0111 +7 In this table the 1 at the far left represents -8 (negative 8). Make sure that you understand this concept Note that the range is still 2 4 = 16 numbers = -8 to +7 Two’s Complement

5. Range and Accuracy of Two’s Complement 1. The range of numbers which can be stored depends on the number of bits being used. 4 bit numbers have a range 8 bit numbers have a range -8 to +7 -128 to +127 3. Numbers stored using two’s complement are always 100% accurate . 2. In a modern computer 32 bits are used stored integers. This gives a range of 2 32 around -2,147,483,648 to +2,147,483,647

6. 8 Bit Two’s complement numbers Here is an example of how to work out the Two’s complement for the number -80 -80 = -128 64 32 16 8 4 2 1 1 0 0 1 1 0 0 0 1. The number is negative so put a 1 in the first column. 128 80 48 2. Subtract the 80 from 128. 3. Now make 48 from the remaining columns using normal binary rules. 32 16 16 0