Question

In most programming languages where integral datatypes have a finite range,there is always one more negative number than positive numbers.

For instance,in C,a byte is -128~127, and an int is between -2^31 and 2^31-1 inclusively.
Is there a reason why a byte is not -127~128,since positives occur more frequently in intuitive sense?

Answer 1

the largest positive is 0111 1111 = 127

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
 0  | 1  |  1 |  1 | 1 | 1 | 1 | 1 |

The largest Negative byte is 1000 0000 = -128

-128| 64 | 32 | 16 | 8 | 4 | 2 | 1 |
 1  | 0  |  0 |  0 | 0 | 0 | 0 | 0 |

In binary the MSB(Most Significant Bit – the front one) is reserved to signify a negative number. The concept is called Twos’ Complement and is used by most computers as a way of representing integers in binary(base 2) notation.

To get more info look into binary calculations