1. Memory addresses

Memory Addresses

Word (Memory)

The storage cells of memory are of a regular and fixed size known as a word. In exams, take a word to be $16\text{ bits}$.

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Words in memory are arranged in groups known as blocks, which are different sizes depending on the system.

A memory address uniquely identifies a word and is composed of two fields:

• $\text{Block field}$: which block the word is in
• $\text{Offset field}$: where the word is within the block Also referred to as the word field.

$$\begin{array}{rl}\text{Block }00& \{\begin{array}{l}\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\begin{array}{c}00101101\\ 01111100\\ 10000111\\ 10101111\end{array}\begin{array}{c}\\ \leftarrow \text{Address }0001\\ \\ \end{array}\end{array}\\ \text{Block }01& \{\begin{array}{l}\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\begin{array}{c}00101101\\ 01111100\\ 10000111\\ 10101111\end{array}\begin{array}{c}\leftarrow \text{Address }0100\\ \\ \\ \leftarrow \text{Address }0111\end{array}\end{array}\\ \text{Block }10& \{\begin{array}{l}\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\begin{array}{c}00101101\\ 01111100\\ 10000111\\ 10101111\end{array}\end{array}\\ \text{Block }11& \{\begin{array}{l}\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\begin{array}{c}00101101\\ 01111100\\ 10000111\\ 10101111\end{array}\begin{array}{c}\\ \\ \\ \leftarrow \text{Address }1111\end{array}\end{array}\end{array}$$

title: Example
Assume a memory consists of $2^{14}$ words and each block has $8$ words.
1. How many blocks does main memory have?
   $$
   	\text{blocks} = \frac{\text{number of words}}{\text{block size}} = \frac{2^{14}}{2^3} = 2^{11}
   $$
2. How many bits does an address have?
   We need to uniquely identify every word in the system.
   $$
   	\text{bits} = \lceil \log_2 (2^{14}) \rceil = 14 \text{ bits}
   $$
3. What are the field sizes of the address?
   $11$ bits to identify block, $3$ bits for the offset.