C has a method for telling the compiler whether a number is in decimal, hexadecimal or octal. That’s base 10, base 16 and base 8. If I want to assign a number to a variable I have my choice of those three number systems. If I’m interested in binary numbers, I’d have to make up some code to deal with it. You can’t assign a binary number to a variable directly.
Since C++ builds on C, the same notation applies.
I wrote some test code to confirm how it works. What’s interesting is the output for negative numbers in hex and octal. Have a look.
Test Code.
I created a console application in Visual C++ 2010 to test the code.
// The standard library includes the system function.
#include <cstdlib>
// C++ standard I/O library
#include <cstdio>
//
int main()
{
int x;
printf("printf Specifiers\n\n", x);
printf("Decimal numbers: %%d (integers)\n");
printf("Hex numbers: %%x or %%X (lowercase, uppercase)\n");
printf("Octals: %%o \n\n");
printf("Positive numbers \n\n", x);
// Decimal 10.
x = 10;
printf("Assign x = 10; \n");
printf("Here is a decimal number: %d \n\n", x);
// Hex equiv.
x = 0x0A;
printf("Assign x = 0x0A; \n");
printf("Hex numbers begin with 0x (zero X). \n");
printf("Here is the hex equivalent: %X \n", x);
printf("Not sure why it's not diplaying as 0x0A. \n\n", x);
// Octal. Starts with zero.
x = 012;
printf("Assign x = 012; \n");
printf("Here is the octal equivalent: %o \n", x);
printf("Octals beging with '0' (zero). \n\n\n", x);
printf("Negative numbers \n\n", x);
x = -10;
printf("Assign x = -10; \n");
printf("Here is a decimal number: %d \n\n", x);
x = -0x0A;
printf("Assign x = -0x0A; \n");
printf("Here is the hex equivalent: %X \n", x);
printf("The minus sign goes before everything as in -0x0A.\n\n", x);
printf("Assign x = -012; \n");
printf("Here is the octal equivalent: %o \n\n", x);
x = 0xfffffff6;
printf("Assign x = 0xfffffff6; \n");
printf("Here is a decimal number: %d \n", x);
printf("Here is the hex equivalent: %X \n", x);
printf("Here is the octal equivalent: %o \n\n", x);
x = 10;
printf("Assign x = 10; \n");
printf("Here is a decimal number: %d \n", x);
printf("Here is the hex equivalent: %X \n", x);
printf("Here is the octal equivalent: %o \n", x);
// keep console window open
system("pause");
// return some value
return 0;
} // end main
Minus ten in decimal is -10, but in hex it’s FFFF FFF6 and in octal it’s 37 777 777 766. Those look like junk numbers, but they are all -10. Here’s why.
A signed integer uses the two’s complement binary number system. That means the left most bit is used as a sign bit (0 for positive and 1 for negative). The remaining bits are used to represent the number.
To simplify things. I’ll use an 8-bit integer. Here’s the layout.
Each bit represents a power of 2. From right to left it's:
7 6 5 4 3 2 1 0
128 64 32 16 8 4 2 1
If I add up all those numbers (128 to 1) I get 255. So, 0 to 255 is 256 possible signed numbers. The maximum number of combinations is 2^8 or 256.
Plus seven in binary is: 0 0 0 0 0 1 1 1
7 6 5 4 3 2 1 0
0 0 0 0 0 4 2 1
The sum of 4, 2, 1 is 7 or 0x07 or 07
The largest negative number is 2^(8-1) or 128. The largest positive number is 2^(8-1)-1 or 127. The range is therefore -128 to 127.
7 6 5 4 3 2 1 0
128 64 32 16 8 0 0 1
The sum of those numbers is: 249. When you subtract 256 (2^8) you end up with -7 or 0xF9 or 0371.
You can alternatively add the numbers this way.
7 6 5 4 3 2 1 0
-128 64 32 16 8 0 0 1 
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