5.11 Hexadecimal and Octal Constants

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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 174 ₁₀ . Computers deal with binary (base 2) numbers: 10101110 ₂ . The octal (base 8) system easily converts to and from binary. Each group of three digits (2 ³ = 8) can be transformed into a single octal digit. Thus 10101110 ₂ can be written as 10 101 110 and changed to the octal 256 ₈ . Hexadecimal (base 16) numbers have a similar conversion, but 4 bits at a time are used. For example, 10010100 ₂ is 1001 0100, or 94 ₁₆ .

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); } 

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