Cyclic Nature

Cyclic nature of data type in C:

In C some data types shows one special properties that when we 
assign a value beyond range of that data type then it will not any 
compiler error but assign a number according to some cyclic order. 
This property is known as cyclic nature of data type.

Data type which shows cyclic nature:

(a) char

(b) int

(c) long int

Data type which doesn't show cyclic nature:

(a) float

(b) double

(c) long double

1. Cyclic nature of unsigned char:

Range of unsigned char is 0 to 255. 
If we will assign a value greater than  255 then value of variable will be 
changed to a value if we will move clockwise direction 
as shown in the figure according to number. 
If number is less than 0 then move in anti clockwise direction.

Short cut formula to find cyclic value:

If number is X where X is greater than 255 then
New value = X % 256
If number is Y where Y is less than 0 then
New value = 256 – (Y% 256)

2. Cyclic nature of signed char:

Range of unsigned char is -128 to 127. 
If we will assign a value greater than 127 then value of variable will be 
changed to a value if we will move clockwise direction 
as shown in the figure according to number. 
If number is less than -128 then move in anti clockwise direction.

Short cut formula to find cyclic value:

If number is X where X is greater than 127 then
p = X % 256
if p <=127 
New value = p 
else 
New value = p – 256
If number is Y where Y is less than -128 then
p = Y % 256 
If p <= 127 
New value = -p 
else 
New value = 256 -p

3. Cyclic nature of unsigned int:

Range of unsigned int is 0 to 653535. 
If we will assign a value greater than 65535 then value of variable will be 
changed to a value if we will move clockwise direction 
as shown in the figure according to number. 
If number is less than 0 then move in anti clockwise direction.

Short cut formula to find cyclic value:

If number is X where X is greater than 65535 then
New value = X % 65536
If number is Y where Y is less than 0 then
New value = 65536– (Y% 65536)

4. Cyclic nature of signed int:

Range of unsigned int is -32768 to 32767. 
If we will assign a value greater than 32767 then value of variable will be 
changed to a value if we will move clockwise direction 
as shown in the figure according to number. 
If number is less than -32768 then move in anti clockwise direction.

If number is X where X is greater than 32767 then

p = X % 65536
if p <=32767 
New value = p 
else 
New value = p - 65536 
If number is Y where Y is less than -32768 then 
p = Y % 65536 
If p <= 32767 
New value = -p 
else 
New value = 65536 -p 

Note: Same rule is also applicable in case of signed long int and 
unsigned long int.