# Solving 16 KB Memory with 16 Bit Wordsize

• WolfpackPride
In summary, a 16 KB memory with a 16 bit wordsize can store 8192 16-bit words, which is equivalent to 2^13 words or 2e13 words.
WolfpackPride

## Homework Statement

A 16 KB memory has a 16 bit wordsize. How many 16 bit words total can be stored in this memory?

None given

## The Attempt at a Solution

I tried many things. My answer were 2e12, 2e13, and 2e14. All of these were wrong. Please help soon (if you can. I only have until midnight and have been working on this for over a day. It's not that difficult but I just can't get it.

A byte is generally 8bits.
KB (at least in computers) means 1024bytes

Yea, I remember that but I am still not sure how to find how many 16 bit words can be stored.

Wait a second...would I just multiply 1024 times 16? It's not neccesarily the math, but rather the terminology that is confusing me. 16KB = 1024bytes(16) = 16384 bytes but is that how many "16 bit words that can be stored" They're asking for the answer in terms of "words" which is really tripping me up. Any more guidance?

16KB is 16*1024 bytes, each byte is 8 bits so a 16bit word is two bytes.
So how many 2 bytes in 16*1024bytes.

Alternately 16KB is 16*1024*8 bits, so how many 16bits in this

When I do that, I get 131072. However, is this in terms of words?

Maybe a new tactic is needed here. This is akin to a question saying that you've got 144 eggs, how many dozen eggs is that?

Now, how many bits in 16 KB? If in that 16 KB of memory, you stored 16-bit variables, how many variables could you store?

Now convert that into base-2

MATLABdude said:
Maybe a new tactic is needed here. This is akin to a question saying that you've got 144 eggs, how many dozen eggs is that?

Now, how many bits in 16 KB? If in that 16 KB of memory, you stored 16-bit variables, how many variables could you store?

Now convert that into base-2

Bits in 16KB?

1KB=1024 bytes
1 byte = 8 bits

16(1024)=16384bytes
16384bytes*(8 bits / 1 byte) = 131072 bits

If in that 16 KB of memory, you stored 16-bit variables, how many variables could you store?

(131072 bits / 16 bits variables) = 8192

Now convert that into base-2

so the solution should be = 2e13 words (8192 words), right? In base 2: 100000000

I previously tried 2e13 and it said that was wrong, is this an error on my part (syntax etc) or is that not the answer? Should I try 10000000 (words) instead?

Thank You, I got it. What I had typed in was 2e13 waaay back when I was first submitting this. I meant 2^13. BIGG difference 8192 vs 2000000000...

Last edited:

## 1. What is the difference between memory size and word size?

The memory size refers to the amount of storage capacity in a computer's memory, while the word size refers to the number of bits that can be accessed and processed at one time by the computer's CPU.

## 2. Why is it important to match the memory size and word size?

If the memory size is larger than the word size, the CPU will have to split the data into smaller chunks, which slows down the processing speed. If the word size is larger than the memory size, it may result in wasted space and inefficient use of resources.

## 3. What challenges are involved in solving 16 KB memory with 16 bit word size?

The main challenge is fitting all the necessary data and instructions into the limited memory space. This requires careful memory management and optimization techniques to ensure efficient use of the available memory.

## 4. How does increasing the word size affect memory usage?

Increasing the word size allows for larger chunks of data to be processed at once, which can improve processing speed and efficiency. However, it also means that each data element will take up more memory space, potentially leading to higher memory usage and cost.

## 5. Can 16 KB memory with 16 bit word size handle complex tasks?

It depends on the complexity and size of the task. With careful optimization and efficient use of memory, it is possible to handle some complex tasks with 16 KB memory and a 16 bit word size. However, for more demanding tasks, a larger memory size and word size may be necessary.

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