5.11 Hexadecimal and Octal Constants

Integer numbers are specified as a string of digits, such as 1234, 88, -123, and so on. These are decimal (base 10) numbers: 174 or 174₁₀. Computers deal with binary (base 2) numbers: 10101110₂. The octal (base 8) system easily converts to and from binary. Each group of three digits (2³ = 8) can be transformed into a single octal digit. Thus 10101110₂ can be written as 10 101 110 and changed to the octal 256₈. Hexadecimal (base 16) numbers have a similar conversion, but 4 bits at a time are used. For example, 10010100₂ is 1001 0100, or 94₁₆.

The C++ language has conventions for representing octal and hexadecimal values. Leading zeros are used to signal an octal constant. For example, 0123 is 123 (octal) or 83 (decimal). Starting a number with "0x" indicates a hexadecimal (base 16) constant. So 0x15 is 21 (decimal). Table 5-3 shows several numbers in all three bases.

Table 5-3. Integer examples

Base 10	Base 8	Base 16
6	06	0x6
9	011	0x9
15	017	0xF
23	027	0x17

Question 5-3: Why does the following program fail to print the correct Zip code? What does it print instead?

#include <iostream>
long int zip;         // Zip code

int main(  )
{
    zip = 02137L;       // Use the Zip code for Cambridge MA

    std::cout << "New York's Zip code is: " << zip << '\n';
    return(0);
}