Memory

Key Terms

• Bit

Short for binary digit, a bit is a fundamental unit of information in Computer Science that represents a state with one of two values, typically 0 and 1.

Any data stored in a computer is, at the most basic level, represented in bits.

• Byte

A group of eight bits. For example, 01101000 is a byte.
A single byte can represent up to 256 data values (2⁸).
Since a binary number is a number expressed with only two symbols, like 0 and 1, a byte can effectively represent all the numbers between 0 and 255, inclusive, in binary format.

The following bytes represents the numbers 1, 2, 3 and 4 in binary format.

1: 00000001
2: 00000010
3: 00000011
4: 00000100

Every place from right to left (google for endianness if you are interesting why it’s so) represent 2ⁿ starting from 0.

• Fixed-Width Integer

An integer represented by a fixed amount of bits. For example, a 32-bit integer is an integer represented by 32 bits (4 bytes), and a 64-bit integer is an integer represented by 64 bits (8 bytes).
The following is the 32-bit representation of the number 1, with clearly separated bytes.
00000000 00000000 00000000 00000001

The following is the 64-bit representation of the number 10, with clearly separated bytes.
00000000 00000000 00000000 00000000 00000000 00000000 00000000 00001010

Regardless of how large an integer is, its fixed-width-integer representation is, by definition, made up of a constant number of bits.
It follows that, regardless of how large an integer is, an operation performed on its fixed-width-integer representation consists of a constant number of bits manipulations,
since the integer is made up of a fixed number of bits. So integer equal 1 will take same amount of memory as 2147483647.

Memory

Broadly speaking, memory is the foundational layer of the computing, where all data is stored.

It’s important to note the following points:

• Data stored in memory is stored in bytes and, by extension, bits.
• Bytes in memory can “point” to other bytes in memory, to store references to other data.
• The amount of memory that machine has is bounded, making it valuable to limit how much memory an algorithm takes up.
• Accessing a byte or a fixed number of bytes (like 4 bytes or 8 bytes in the case of 32-bit and 64-bit integers) is an elementary operation, which can be loosely treated as a single unit of operational work.
• Memory slot, can fit 8-bits which is 1 byte. For example 32-bit integer would take 4 memory slots.
• Memory slot can store address to another memory slot, that’s called a pointer.
• When you are storing integer, its typically fix-width integer, means It’s either 8/16/32/64 bit. Point is we know how many bytes it will take up.
• If it takes more than one memory slot it’s going to have to be stored however many memory slots are needed to store it. Back to back and free.
• Storing list work similar, if you’re going to want to store list of five 32-bit integers, for instance, that’s list it’s going to have 20 memory slots.