Binary Background

Normally, a programmer can think in terms of base ten numbers.

However, a compiler must allocate some finite quantity of bits (e.g., 32 bits) for a variable, and that quantity of bits limits the range of numbers that the variable can represent.

Thus, understanding how the quantity of bits influences a variable's number range is useful.

Because each memory location is composed of bits (0s and 1s), a processor stores a number using base 2, known as a binary number.

For a number in the more familiar to humans is base 10, known as a decimal number, each digit must be 0-9 and each digit's place is weighed by increasing powers of 10. So the decimal number 212 represents (2 * 10^2) + (1 * 10^1) + (2 * 10^0) = (2 * 100) + (1 * 10) + (2 * 1) = 200 + 10 + 2 = 212.

In base 2, each digit must be 0 or 1 and each digit's place is weighed by increasing powers of 2. So the binary number 1101 represents (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) Which is equivalent (in base 10) as (1 * 8) + (1 * 4) + (0 * 2) + (1 * 1) = 8 + 4 + 0 + 1 = 13.

Check out this visual

Behind the scenes

The compiler translates decimal numbers into binary numbers before storing the number into a memory location.

For example: The compiler would convert the decimal number 212 to the binary number 11010100, meaning (1 * 128) + (1 * 64) + (0 * 32) + (1 * 16) + (0 * 8) + (1 * 4) + (0 * 2) + (0 * 1), and stores that binary number in memory.