Clarification is needed on bitwise not (~) operator

Suppose you have the following C code.

 unsigned char a = 1;

 printf("%d\n", ~a); // prints -2
 printf("%d\n", a); // prints 1

I am surprised to see -2 printed as a result of ~1 conversion:

The opp开发者_StackOverflowosite of 0000 0001 is 1111 1110. That is anything but -2.

What am I missing here?

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It is two's complement.

In two's complement representation, if a number x's most significant bit is 1, then the actual value would be −(~x + 1).

For instance,

0b11110000 = -(~0b1111 + 1) = -(15 + 1) = -16.

This is a natural representation of negative numbers, because

0000001 =  1
0000000 =  0
1111111 = -1  (wrap around)
1111110 = -2
1111101 = -3 etc.

See http://en.wikipedia.org/wiki/Two%27s_complement for detail.

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BTW, to print an unsigned value, use the %hhu or %hhx format. See http://www.ideone.com/YafE3.

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%d stands for signed decimal number, not unsigned. So your bit pattern, even though it is stored in an unsigned variable, is interpreted as a signed number.

See this Wikipedia entry on signed number representations for an understanding of the bit values. In particular see Two's complement.

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One (mildly humorous) way to think of signed maths is to recognize that the most significant bit really represents an infinite number of bits above it. So in a 16-bit signed number, the most significant bit is 32768+65536+131072+262144+...etc. which is 32768*(1+2+4+8+...) Using the standard formula for a power series, (1+ X + X^2 + X^3 +...) = 1/(1-X), one discovers that (1+2+4+8+...) is -1, so the sum of all those bits is -32768.