This chapter examined how modern computers represent information using bits and bytes. An important takeaway is that a computer’s memory stores all information as binary 0’s and 1’s — it’s up to programs or the people running them to interpret the meaning of those bits. This chapter primarily focused on integer representations, beginning with unsigned (non-negative) integers before considering signed integers.

Computer hardware supports a variety of operations on integers, including the familiar addition, subtraction, multiplication, and division. Systems also provide bitwise operations like bitwise AND, OR, NOT, and shifting. When performing any operation, consider the number of bits used to represent the operands and result. If the storage space allocated to the result isn’t large enough, an overflow may misrepresent the resulting value.

Finally, this chapter explored common schemes for representing real numbers in binary, including the standard IEEE 754 standard. Note that when representing floating-point values, we sacrifice precision for increased flexibility (i.e., the ability to move the decimal point).