Numbers are not necessarily stored in a computer with perfect precision. Each number is allowed only a certain number of bits for storage.
Usually integers are stored accurately with a limited range. Real numbers are stored with a large range but less accuracy (using floating-point representation).
As the numbers are all positive no sign bit is necessary.
The largest number which can be stored in a register with n bits is 2n – 1.
The smallest number which can be stored is 0 .
For an eight-bit word the largest number possible = 111111112
=1000000002-1=28-1 (=255)
If twos complement integers are represented in a register or location of n bits, then the largest positive number possible = 2n -1-1
the most negative number possible = -2n -1-1
For an eight-bit word the largest number possible =01111111 (as the first bit is a sign bit)
=27-1 (=127)
The most negative number
=100000002 (first bit=1 to get a negative number; as we are complementing negative numbers, the other bits should be as small as possible i.e. 0)
This represents -(11111112+ 1) (Taking twos complement)
= -100000002
= -27 (=-128)
i.e. The range of twos complement integers in an eight-bit register is -128 to 127
Binary integers are represented using twos complement notation in a 16-bit register. Find their range.
Largest positive integer is 01111111111111112=215-1
= 32 767
Most negative integer is 1000 0000 0000 00002 = -(111 1111 111111112+ 1)
= -1000 0000 0000 0000
=215
= -32768
i.e. The integers represented. lie in the range -32 768 to +32 767 inclusive
Labels: Computer