# Confused on how they figured out bytes, book example:

• mr_coffee
In summary, the Intrinsity caches have a capacity of 16 KB and are divided into 256 blocks with 16 words per block. This means that the total data size is 64 bytes, which is equal to 512 bits. The tag field for each block is 18 bits, calculated by subtracting 8 bits (representing a byte) and 6 bits (possibly representing the block size in powers of 2) from the total 32 bits of the address. The total number of bits for the cache is calculated by multiplying 256 (the number of blocks) by the data size (512 bits) and adding the tag field (18 bits) and a valid bit (1 bit) for each block, resulting

#### mr_coffee

The Intrinsity caches are 16 KB caches and have 256 blocks with 16 words per block.

Thus data is 64 bytes = 512 bytes.
The tag field is 18 bits (32 - (8 + 6)).
Total bits = 256 x (Data + Tag + Valid)
= 256 x (512 bits + 18 bits + 1 bit)
= 135,936 bitsI'm confused on how they got 64 bytes then said = 512 bytes.

Also where did they get (32 - (8+6))?
I think i know where they got 32, because its a 32 bit address.Thank you.

I took 16E3/265 = 62.5 not 64.

EDIT:

Okay I got alittle farther...

16E3/16 = 1000 which is ~ 2^10 words, and with a block size of 4 words (2^2), but still not sure how they got 64 and 512, nor the (8+6).

Last edited:
64 bytes = 512 bits

Isn't that just what they meant?

16KB is not 16E3 but 16*1024.
16*1024/16 is not ~ but = 2^10.

Ahhh thanks guys!

that makes sense... it was a typo in the book.
okay so I understand the 512 bits.

for the:
The tag field is 18 bits (32 - (8 + 6)).
Total bits = 256 x (Data + Tag + Valid)

32 bits address, is the 8 because 8 bits in a byte? still not seeing the 6 though.

Also is the 256 x (data + tag + valid) because they said there is 256 blocks?

## 1. How exactly are bytes calculated?

Bytes are calculated by using a base-2 numeral system, also known as binary. Each byte is made up of 8 bits, and each bit can have a value of 0 or 1. By combining 8 bits in different ways, we can create different values and characters.

## 2. What is the relationship between bytes and bits?

Bytes and bits are closely related, as a byte is made up of 8 bits. However, they serve different purposes. Bits are used to represent individual values or characters, while bytes are used to represent larger chunks of data.

## 3. How did bytes become the standard unit of measurement for data?

Bytes became the standard unit of measurement for data storage due to the popularity of the binary system. It was also adopted by early computer systems, and has remained the standard unit ever since.

## 4. Can bytes be converted to other units of measurement?

Yes, bytes can be converted to other units of measurement such as kilobytes, megabytes, and gigabytes. Each unit is a multiple of 1024, so 1 kilobyte is equal to 1024 bytes, 1 megabyte is equal to 1024 kilobytes, and so on.

## 5. How are bytes used in everyday technology?

Bytes are used in everyday technology for data storage, transmission, and processing. They are used to store files on computers, transfer data through the internet, and run programs and applications. Without bytes, modern technology as we know it would not be possible.