1.计算机内部存储是按补码的形式存储的,最高位为0表示正数,其原码就是补码本身.
最高位为1表示负数.而0占一个补码的(000 ... 000).这就是为什么正数少一个,因为0的最高位也是0.
2.根据补码最小负数应该是(以8位举例)10000000(按位取反为1111 1111,再加1为1000 0000,真值为-256)
3.还是按位取反再加1 1000 0000 --->1111 1111--->1000 0000(真值-256此时,最高位是符号位也是数值位).

注意一下在真值1000 0000表示的时候最高位1是数值位.而补码不同(应该按照转换规则,是什么就是什么).

Upstair is right!

complementarity:
// Numeric.cpp
#include <iostream>
#include <limits>

using namespace std;

int main() {
cout << " 1 The minimum value for char is " <<
(int)numeric_limits<char>::min() << endl;
cout << " 2 The minimum value for int is " <<
numeric_limits<int>::min() << endl;
cout << " 3 The maximum value for char is " <<
(int)numeric_limits<char>::max() << endl;
cout << " 4 The maximum value for int is " <<
numeric_limits<int>::max() << endl;
cout << " 5 The number of bits to represent a char is " <<
numeric_limits<char>::digits << endl;
cout << " 6 The number of bits to represent an int is " <<
numeric_limits<int>::digits << endl;
cout <<" 7 The number of digits representable in base 10 for float is "
<< numeric_limits<float>::digits10 << endl;
cout << " 8 Is a char signed? " <<
numeric_limits<char>::is_signed << endl;
cout << " 9 Is an unsigned integer signed? " <<
numeric_limits<unsigned int>::is_signed << endl;
cout << "10 Is an integer an integer? " <<
numeric_limits<int>::is_integer << endl;
cout << "11 Is a float an integer? " <<
numeric_limits<float>::is_integer << endl;
cout << "12 Is an integer exact? " <<
numeric_limits<int>::is_exact << endl;
cout << "13 Is a float exact? " <<
numeric_limits<float>::is_exact << endl;
cout << "14 The radix for float is " <<
numeric_limits<float>::radix << endl;
cout << "15 The epsilon for float is " <<
numeric_limits<float>::epsilon() << endl;
cout << "16 The round error for float is " <<
numeric_limits<float>::round_error() << endl;
cout << "17 The minimum exponent for float is " <<
numeric_limits<float>::min_exponent << endl;
cout << "18 The minimum exponent in base 10 " <<
numeric_limits<float>::min_exponent10 << endl;
cout << "19 The maximum exponent is " <<
numeric_limits<float>::max_exponent << endl;
cout << "20 The maximum exponent in base 10 " <<
numeric_limits<float>::max_exponent10 << endl;
cout << "21 Can float represent positive infinity? " <<
numeric_limits<float>::has_infinity << endl;
cout << "22 Can double represent positive infinity? " <<
numeric_limits<double>::has_infinity << endl;
cout << "23 Can int represent positive infinity? " <<
numeric_limits<int>::has_infinity << endl;
cout << "24 Can float represent a NaN? " <<
numeric_limits<float>::has_quiet_NaN << endl;
cout << "25 Can float represent a signaling NaN? " <<
numeric_limits<float>::has_signaling_NaN << endl;
cout << "26 Does float allow denormalized values? " <<
numeric_limits<float>::has_denorm << endl;
cout << "27 Does float detect denormalization loss? " <<
numeric_limits<float>::has_denorm_loss << endl;
cout << "28 Representation of positive infinity for float " <<
numeric_limits<float>::infinity() << endl;
cout << "29 Representation of quiet NaN for float " <<
numeric_limits<float>::quiet_NaN() << endl;
cout << "30 Minimum denormalized number for float " <<
numeric_limits<float>::denorm_min() << endl;
cout << "31 Minimum positive denormalized value for float " <<
numeric_limits<float>::denorm_min() << endl;
cout << "32 Does float adhere to IEC 559 standard? " <<
numeric_limits<float>::is_iec559 << endl;
cout << "33 Is float bounded? " <<
numeric_limits<float>::is_bounded << endl;
cout << "34 Is float modulo? " <<
numeric_limits<float>::is_modulo << endl;
cout << "35 Is int modulo? " <<
numeric_limits<float>::is_modulo << endl;
cout << "36 Is trapping implemented for float? " <<
numeric_limits<float>::traps << endl;
cout << "37 Is tinyness detected before rounding? " <<
numeric_limits<float>::tinyness_before << endl;
cout << "38 What is the rounding style for float? " <<
(int)numeric_limits<float>::round_style << endl;
cout << "39 What is the rounding style for int? " <<
(int)numeric_limits<int>::round_style << endl;
cout << "40 How does a float represent a signaling NaN? " <<
numeric_limits<float>::signaling_NaN() << endl;
cout << "41 Is int specialized? " <<
numeric_limits<float>::is_specialized << endl;
}
////////////////////////////////////////////////////////////////////////////
Output

1 The minimum value for char is -128
2 The minimum value for int is -2147483648
3 The maximum value for char is 127
4 The maximum value for int is 2147483647
5 The number of bits to represent a char is 7
6 The number of bits to represent an int is 31
7 The number of digits representable in base 10 for float is 6
8 Is a char signed? 1
9 Is an unsigned integer signed? 0
10 Is an integer an integer? 1
11 Is a float an integer? 0
12 Is an integer exact? 1
13 Is a float exact? 0
14 The radix for float is 2
15 The epsilon for float is 1.19209e-007
16 The round error for float is 0.5
17 The minimum exponent for float is -125
18 The minimum exponent in base 10 -37
19 The maximum exponent is 128
20 The maximum exponent in base 10 38
21 Can float represent positive infinity? 1
22 Can double represent positive infinity? 1
23 Can int represent positive infinity? 0
24 Can float represent a NaN? 1
25 Can float represent a signaling NaN? 1
26 Does float allow denormalized values? 1
27 Does float detect denormalization loss? 1
28 Representation of positive infinity for float 1.#INF
29 Representation of quiet NaN for float 1.#QNAN
30 Minimum denormalized number for float 1.4013e-045
31 Minimum positive denormalized value for float 1.4013e-045
32 Does float adhere to IEC 559 standard? 1
33 Is float bounded? 1
34 Is float modulo? 0
35 Is int modulo? 0
36 Is trapping implemented for float? 1
37 Is tinyness detected before rounding? 1
38 What is the rounding style for float? 1
39 What is the rounding style for int? 0
40 How does a float represent a signaling NaN? 1.#QNAN
41 Is int specialized? 1