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Memory Specifications
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Today, we're going to discuss memory specifications, starting with how to understand memory sizes such as 16KΓ8. Can anyone tell me what this means?
I think it means there are 16K words, each with 8 bits?
Great job! Yes, that means there are 16,384 words of data, and each word consists of 8 bits. Can anyone calculate how many memory cells are in total?
So if we multiply 16,384 words by 8 bits, we get 131,072 bits, right?
Exactly! That's how many bits are stored across the complete memory. Remember, the formula you can use is: Total Memory Cells = Number of Words Γ Bits per Word.
Could we use a mnemonic for this?
Absolutely! Let's use 'WBM' β Words, Bits, Multiply! This can help you remember the process while calculating memory specifications.
That's helpful; I can remember that already!
Alright, to sum up, when you see a memory spec like 16KΓ8, recognize you're looking at both the word size and the total storage, which we calculate by total bits.
Address and Data Lines
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Next, letβs take a look at another example: a memory specified as 32KΓ8. Who can tell me how to determine the number of address lines for this memory?
Shouldn't we use the formula for address lines, based on the number of words?
That's correct! Address lines can be calculated using the formula 2^n = Number of Addresses. So, for 32K, we need to find out what n gives us 32K.
That would be 15, because 2^15 is 32,768!
Right again! And how about the data lines? Who recalls how many data lines are necessary in this specification?
For 32KΓ8, we have 8 bits, so that means we'll need 8 data lines?
Precisely! You have itβ8 data lines. So, in summary, you can remember this as 'D-Lines for Data' to connect the number of bits with data lines.
RAM Configuration
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Now letβs visualize constructing a RAM configuration: we want to build a 64KΓ16 RAM using 16KΓ8 chips. How would we approach this?
We would need to divide the total required capacity by the capacity of one chip, right?
Exactly! If 64K is needed and each chip stores 16K, how many chips do we need?
Thatβs 4 chips, since 64K divided by 16K is 4!
Great! And as for the width of each RAM chip? Weβll need to combine two chips in parallel for the data lines, as each chip is only 8 bits.
So are we talking about needing two chips to make 16 bits?
You're right! You can remember this as 'Chip Count Equals Total Capacity Divided by Each Chipβs Size.'
That's a straightforward way to look at it!
Introduction & Overview
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Quick Overview
Standard
The Problems section offers a series of practical exercises that challenge students to calculate memory attributes based on specifications. These problems enhance understanding of memory organization including bits per word, address lines, and storage capacity.
Detailed
Detailed Summary
The Problems section comprises several computational exercises designed to assess a student's understanding of memory specifications in computer systems. The problems include calculations related to various memory types, such as determining the number of bits, words, and memory cells in specific configurations. The exercises cover different memory sizes and types, providing an opportunity for students to demonstrate their skills in addressing memory architecture problems.
In the first exercise, students tackle a memory designated as 16KΓ8, asking them to compute the bits per word, total words, and memory cells. The second problem involves a 32KΓ8 memory specification, requiring students to determine the number of address lines, data input lines, and the type of decoder. Additional exercises involve constructing a specific RAM configuration and analyzing hard disk specifications. These problems are crucial for reinforcing concepts discussed throughout the chapter while providing practical, real-world application scenarios.
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Audio Book
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Problem 1: Memory Specification
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- A certain memory is specified as 16KΓ8. Determine (a) the number of bits in each word, (b) the number of words being stored and (c) the number of memory cells.
(a) 8; (b) 16384; (c) 131072
Detailed Explanation
This problem involves understanding memory specifications. The term '16KΓ8' means the memory can store 16K words, where each word consists of 8 bits.
1. Bits in Each Word: Since it's specified as 8, each word contains 8 bits.
2. Number of Words Being Stored: '16K' means 16 Kilowords, where K represents 1024. Thus, 16K equals 16 x 1024 = 16384 words.
3. Number of Memory Cells: Each word consists of 8 bits, and with 16384 words, you have 16384 words x 8 bits = 131072 bits in total. Thus, the total number of memory cells (bits) is 131072.
Examples & Analogies
Imagine a library where each book contains 8 pages (bits) and the library has 16K books. If each book is a word, then the total number of pages in the library would be the total memory cells, which is much larger than the number of books alone.
Problem 2: Memory Lines and Decoder
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- A certain memory is specified as 32KΓ8. Determine (a) the number of address input lines, (b) the number of data input lines, (c) the number of data output lines and (d) the type of decoder.
(a) 15; (b) 8; (c) 8; (d) 1-of-15 decoder
Detailed Explanation
For this problem, we analyze a memory with the specification '32KΓ8'.
1. Address Input Lines: To determine how many address lines are needed to access 32K locations, use log base 2. 32K means 32 x 1024 or 32768. The formula log2(32768) gives about 15 lines.
2. Data Input and Output Lines: The 'Γ8' part tells us that each word is 8 bits wide, so both data input and output lines equal 8.
3. Type of Decoder: A '1-of-15 decoder' means we have one output for each addressable memory location, which corresponds to the number of address lines calculated above.
Examples & Analogies
Think of it like a parking lot: the address lines represent the number of rows you can park your cars in, and with 15 rows (or lines), you can access each parking space (words) directly. In each space, you can fit 8 toy cars (bits of data).
Problem 3: Constructing RAM
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- It is desired to construct a 64KΓ16 RAM from an available RAM chip specified as 16KΓ8. Determine the number of RAM chips required for the same.
8
Detailed Explanation
To create a 64KΓ16 RAM from 16KΓ8 RAM chips, you need to consider the requirements.
1. Target Memory: 64KΓ16 means you need 64K words of 16 bits each. This equals 65536 words with 16 bits.
2. Available Chips: Each 16KΓ8 RAM chip provides 16K words, but each word is only 8 bits. To achieve 16 bits, you would require two chips to work in tandem (doubling capacity).
3. Calculating Number of Chips: The 64K needed, divided by the 16K each chip can meet results in 4 chips for the 64K total. Since we need two chips for each word to meet the 16-bits requirement, you multiply: 4 chips x 2 equals 8 chips in total.
Examples & Analogies
Imagine building a larger bookshelf (64K) using smaller boxes (16K). If each smaller box can only carry a certain number of notebooks (8 books per box), you need additional boxes to stack them, and if you need each shelf to hold two rows of notebooks (16 books), you will end up needing to use more boxes to meet the storage requirement.
Problem 4: Hard Disk Analysis
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- The following data refer to a hard disk: number of tracks per side=600; number of sides=2; number of bytes per sector=512; storage capacity in bytes=21,504,000. Determine the number of sectors per track for this hard disk.
35
Detailed Explanation
In this problem, we have data about a hard disk and need to determine the sectors per track.
1. Total Storage Capacity: The total storage capacity in bytes is given as 21,504,000 bytes.
2. Sector Size: Each sector is 512 bytes. To find the total number of sectors on the hard disk, divide the total capacity by the size of each sector: 21,504,000 Γ· 512 = 42,000 sectors total.
3. Tracks and Sides: Each side of the hard disk has 600 tracks, and since there are 2 sides, the total number of tracks is 600 x 2 = 1200 tracks.
4. Sectors Per Track: To find sectors per track, take total sectors (42,000) and divide by total tracks (1200). This results in 42,000 Γ· 1200 = 35 sectors per track.
Examples & Analogies
Think of a pizza (hard disk) cut into 1200 slices (tracks) with each slice having several pieces of topping (sectors). If you have a lot of topping segments (42,000), you can determine how many pieces of topping each slice will have, giving you the sectors per track.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Memory Size Calculation: Understanding how to calculate bits, words, and memory cells.
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Address and Data Lines: The relationship between memory specifications and required wiring.
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RAM Configuration: The process of utilizing smaller RAM chips to build larger configurations.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example: For a memory specified as 16KΓ8, the storage calculation would yield 8 bits per word, 16,384 total words, and 131,072 bits.
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Example: When constructing a 64KΓ16 RAM from 16KΓ8 chips, you would require 4 chips to meet the capacity.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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Bits multiply, cells are high, calculate memory as you try!
π Fascinating Stories
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Once, there was a chip who wanted to combine forces with friends to become a bigger RAM; together they formed the perfect memory configuration.
π§ Other Memory Gems
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Remember the 'A-D-C' β Address, Data, Combine when working with memory specs.
π― Super Acronyms
C-C-A
- Capacity
- Chips
- Addressing
- key points of memory configurations.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Memory Cell
Definition:
A basic unit of storage in a memory device that can hold a binary digit (bit).
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Term: Address Lines
Definition:
Conductors used to specify the location of data in memory storage.
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Term: Data Lines
Definition:
Conductors used to transfer data between memory and other parts of a computer.
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Term: RAM (Random Access Memory)
Definition:
A type of computer memory that can be accessed randomly, allowing data to be read or written in almost the same amount of time.