There are 4 basic data types in C namely character, integer, floating point number and double precision floating point number(See Table 1). Character(char) and Integer(int) data types either signed or unsigned. The default for char and int is signed i.e. values are distributed between positive and negative values (See Table 2).
Table 1:
Data
Type
|
C
Keyword
|
Storage
size
|
Character
|
char
|
1
bye
|
Integer
|
int
|
2
or 4 bytes
|
Floating
Point
|
float
|
4
bytes
|
Double
precession floating point.
|
double
|
8
bytes
|
Table 2:
Type
|
Storage
size
|
Value
range
|
char
|
1
byte
|
-128 to 127
|
unsigned
char
|
1
byte
|
0 to 255
|
int
|
2
or 4 bytes
|
-32,768 to 32,767
or -2,147,483,648 to 2,147,483,647
|
unsigned
int
|
2
or 4 bytes
|
0 to 65,535 or 0 to
4,294,967,295
|
short
|
2
bytes
|
-32,768 to 32,767
|
unsigned
short
|
2
bytes
|
0 to 65,535
|
long
|
4
bytes
|
-2,147,483,648 to
2,147,483,647
|
unsigned
long
|
4
bytes
|
0 to 4,294,967,295
|
The
standard C specification (ANSI C) does not actually specify a fixed range or
memory for
these data types. All it says is
something like below:
short int <= int <= long int and float <= double <= long double
This means that a short int
should assign less than or the same amount of storage as an int and the int
should be less or the same bytes as a long int. And the above ranges are actually
machine and implementation dependent.
If you want to know the actual size allocated based on your machine, then you can use the sizeof operator. See the following examples:
int main()
{
printf("the size of char is %d bytes\n", sizeof(char));
printf("the size of short is %d bytes\n", sizeof(short));
printf("the size of int is %d bytes\n", sizeof(int));
printf("the size of long is %d bytes\n", sizeof(long));
printf("the size of float is %d bytes\n", sizeof(float));
printf("the size of double is %d bytes\n", sizeof(double));
printf("the size of long double is %d bytes", sizeof(long double));
return 0;
}
Suppose, a 8-bit Unsigned Number represented as follows:
number = 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2 + 2×b1 + 1×b0
For example, if a byte contain 10010001b then the value of a number is
Table 4: 8-bit Unsigned Numbers
In case of a signed number, MSB bit is a sign bit. So for a 8-bit signed number, there are 256 different numbers from -128 to 127.
Similarly, there are 65536 different 16-bit numbers; 0 to 65535 unsigned numbers or -32768 to 32767 signed numbers.
Unsigned 16-bit numbers calculated and represented as follows:
number = 32768×b15 + 16384×b14 + 8192×b13 + 4096×b12 + 2048×b11 + 1024×b10
+ 512×b9 + 256×b8 + 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2
+ 2×b1 + 1×b0
Examples: 16-bit Signed Numbers
Now, what is the difference between signed and unsigned number? Most Significant Bit(MSB) of a number will determine whether a number is signed or unsigned.
MSB
|
LSB
|
||||||
b7
|
b6
|
b5
|
b4
|
b3
|
b2
|
b1
|
b0
|
27
|
26
|
25
|
24
|
23
|
22
|
21
|
20
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
Where, each bit from b0 to b7 contains either 0 or 1. So there are 256 different numbers from 0 to 255 and the value of a numbers calculated as follows:
number = 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2 + 2×b1 + 1×b0
For example, if a byte contain 10010001b then the value of a number is
(128×1+0+0+16×1+0+0+0+1×1) = 145d. See the following table 3 for more examples:
Table 4: 8-bit Unsigned Numbers
Binary
|
Equivalent
Decimal
|
0000
0000
|
0+0+0+0+0+0+0+0 = 0
|
1010
0011
|
128+0+32+0+0+0+2+1 = 163
|
0101
0100
|
0+64+0+16+0+4+0+0 = 84
|
1010 1101
|
128+0+32+0+8+4+0+1 = 173
|
1111 1111
|
128+64+32+16+8+4+2+1 = 255
|
In case of a signed number, MSB bit is a sign bit. So for a 8-bit signed number, there are 256 different numbers from -128 to 127.
MSB
|
LSB
|
||||||
b7
|
b6
|
b5
|
b4
|
b3
|
b2
|
b1
|
b0
|
27
|
26
|
25
|
24
|
23
|
22
|
21
|
20
|
-128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
And the value of a 8-bit signed number calculated as follows:
number = -128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2 + 2×b1 + 1×b0
For Example, if a byte contain 10010001b then the value of a signed number is
number = -128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2 + 2×b1 + 1×b0
For Example, if a byte contain 10010001b then the value of a signed number is
(-128×1+0+0+16×1+0+0+0+1×1) = (-128+16+1) = -111d. See the following table for more examples:
Table 4: 8-bit Signed Numbers
Table 4: 8-bit Signed Numbers
Binary
|
Equivalent
Decimal
|
1000
0000
|
-128+0+0+0+0+0+0+0 = -128
|
1010
0011
|
-128+0+32+0+0+0+2+1 = -93
|
0101
0100
|
0+64+0+16+0+4+0+0 = 84
|
1010 1101
|
-128+0+32+0+8+4+0+1 = -83
|
0111 1111
|
0+64+32+16+8+4+2+1 = 127
|
Similarly, there are 65536 different 16-bit numbers; 0 to 65535 unsigned numbers or -32768 to 32767 signed numbers.
Unsigned 16-bit numbers calculated and represented as follows:
number = 32768×b15 + 16384×b14 + 8192×b13 + 4096×b12 + 2048×b11 + 1024×b10
+ 512×b9 + 256×b8 + 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2
+ 2×b1 + 1×b0
MSB
|
LSB
|
||||||||||||||
b15
|
b14
|
b13
|
b12
|
b11
|
b10
|
b9
|
b8
|
b7
|
b6
|
b5
|
b4
|
b3
|
b2
|
b1
|
b0
|
215
|
214
|
213
|
212
|
211
|
210
|
29
|
28
|
27
|
26
|
25
|
24
|
23
|
22
|
21
|
20
|
32768
|
16384
|
8192
|
4096
|
2048
|
1024
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
Examples: 16-bit
Unsigned Numbers
Signed 16-bit numbers calculated and represented as follows:
number = -32768×b15 + 16384×b14 + 8192×b13 + 4096×b12 + 2048×b11 + 1024×b10
+ 512×b9 + 256×b8 + 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2
+ 2×b1 + 1×b0
Binary
|
Equivalent
Decimal
|
0000000000000000
|
0+0+0+0+0+0+0+0 = 0
|
1100101010100011
|
32768+16384+0+0+2048+0+512+0+128+0+32+0+0+0+2+1
= 51875
|
0000010101001100
|
0+0+0+0+0+1024+0+256+0+64+0+0+8+4+0+0
= 1365
|
1010110010010100
|
32768+0+8192+0+2048+1024+0+0+128+0+0+16+0+4+0+0
= 44180
|
1111111111111111
|
32768+16384+8192+4096+2048+1024+512+256+128+64+32+16+8+4+2+1
= 65535
|
Signed 16-bit numbers calculated and represented as follows:
number = -32768×b15 + 16384×b14 + 8192×b13 + 4096×b12 + 2048×b11 + 1024×b10
+ 512×b9 + 256×b8 + 128×b7 + 64×b6 + 32×b5 + 16×b4 + 8×b3 + 4×b2
+ 2×b1 + 1×b0
MSB
|
LSB
|
||||||||||||||
b15
|
b14
|
b13
|
b12
|
b11
|
b10
|
b9
|
b8
|
b7
|
b6
|
b5
|
b4
|
b3
|
b2
|
b1
|
b0
|
215
|
214
|
213
|
212
|
211
|
210
|
29
|
28
|
27
|
26
|
25
|
24
|
23
|
22
|
21
|
20
|
-32768
|
16384
|
8192
|
4096
|
2048
|
1024
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
Examples: 16-bit Signed Numbers
Binary
|
Equivalent
Decimal
|
1000000000000000
|
-32768+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0 = -32768
|
1100101010100011
|
-32768+16384+0+0+2048+0+512+0+128+0+32+0+0+0+2+1 = -13661
|
0000010101001100
|
0+0+0+0+0+1024+0+256+0+64+0+0+8+4+0+0
= 1356
|
1010110010010100
|
-32768+0+8192+0+2048+1024+0+0+128+0+0+16+0+4+0+0 = -21356
|
0111111111111111
|
0+16384+8192+4096+2048+1024+512+256+128+64+32+16+8+4+2+1
= 32767
|
