The amount of cells in a computer`s main memory

In summary: Hex digits are usually used to represent binary numbers (like 0x1D = 0001 1101 base 2), and the four bits needed to represent a hex digit are just the four bits that are enough to represent all possible hex digits.In summary, if each cell's address in a computer's main memory can be represented by 2 hexadecimal digits, there would be 65,536 bytes available. However, if 4 hexadecimal digits are used, there would be 4,294,967,296 bytes available. Each hex digit can be represented by four bits, and there are sixteen possible values for each hex digit. Therefore, each additional hex digit used in the address would multiply the number of possible locations by sixteen
  • #1
guitar
5
0

Homework Statement



How many cells can be in a computer`s main memory if each cell`s address can be represented by 2 hexadecimal digits? what if 4 hexadecimal digits are used?


Homework Equations



N/A

The Attempt at a Solution



ok, i tried and other people helped and i am stuck with this:

1. If each cell's address is only 2 hex digits, you are using 16 binary digits, and therefore 65,536 bytes.

2. Hexadecimal means base 16. In other words, 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B ,C, D, E, F).
Two hexadecimal digits give you 16 x 16 = 256 locations.
Four hexadecimal digits give you 16 x 16 x 16 x 16 = 65536 locations.

3. 0 (hexadecimal representation) is 0000 (bit pattern)
1 (hexadecimal representation) is 0001 (bit pattern)
2 (hexadecimal representation) is 0010 (bit pattern)
etc etc etc

i am trying to connect the dots here...are those 16 digits in base 16- 16 locations? also are these digits: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B ,C, D, E, F) 4 bits or 8 bits each? or are they just 1 bit each? and how does the hex to bit pattern representation play up into this?

thanks.
 
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  • #2
guitar said:
i am trying to connect the dots here...are those 16 digits in base 16- 16 locations? also are these digits: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B ,C, D, E, F) 4 bits or 8 bits each? or are they just 1 bit each? and how does the hex to bit pattern representation play up into this?
I don't understand what you're asking in your first question. What do you mean "are those 16 digits in base 16- 16 locations?"
Each hex digit can be represented by four bits:
0 = 0000
1 = 0001
2 = 0010
3 = 0011
...
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111

Any hex digit 8 or higher requires 4 bits to represent it. Smaller hex digits could be represented with fewer bits. The only numbers that could be represented with one bit are 0 and 1.
 
  • #3
Mark44 said:
I don't understand what you're asking in your first question. What do you mean "are those 16 digits in base 16- 16 locations?"
Each hex digit can be represented by four bits:
0 = 0000
1 = 0001
2 = 0010
3 = 0011
...
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111

Any hex digit 8 or higher requires 4 bits to represent it. Smaller hex digits could be represented with fewer bits. The only numbers that could be represented with one bit are 0 and 1.

for starters i see 4 digits for all the hex digits from 0 to F. for example bit pattern for the hex digit 3 is 0011(4 bits)...please elaborate on this.
 
  • #4
guitar said:
How many cells can be in a computer`s main memory if each cell`s address can be represented by 2 hexadecimal digits? what if 4 hexadecimal digits are used?
...
1. If each cell's address is only 2 hex digits, you are using 16 binary digits, ...
I don't follow this. Each hex digit specifies four binary digits, so two hex digits specifies (two times four equals) eight binary digits.

guitar said:
2. Hexadecimal means base 16. In other words, 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B ,C, D, E, F).
Yes, there are sixteen possible values for each hex digit.

guitar said:
Two hexadecimal digits give you 16 x 16 = 256 locations.
Four hexadecimal digits give you 16 x 16 x 16 x 16 = 65536 locations.
Doesn't this already answer the original problem?

guitar said:
are those 16 digits in base 16- 16 locations?
I suppose that the sixteen possible values of the least significant digit (LSD :O) distinguish sixteen memory locations, given some fixed value for any other more significant digits. Each additional hex digit in the number multiplies the number of possible distinct values by sixteen. Your wording here is very confusing, though - too many "16"s.

guitar said:
also are these digits: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B ,C, D, E, F) 4 bits or 8 bits each?
You only need up to four bits to specify one of these hex digits. Each hex digit requires four bits.

guitar said:
how does the hex to bit pattern representation play up into this?
I don't know what you're talking about.
 
Last edited:
  • #5


I can provide some clarification on the concept of hexadecimal representation and its relationship to computer memory. First, let's define what a cell in computer memory is. A cell is a unit of storage in computer memory that can hold a single piece of data, such as a number or character. Each cell has a unique address, which is used to access and store data in that cell.

Now, let's talk about hexadecimal representation. As mentioned in the previous response, hexadecimal is a base 16 number system, which means it uses 16 digits (0-9 and A-F) to represent numbers. In contrast, our everyday number system, decimal, uses 10 digits (0-9). The reason why hexadecimal is commonly used in computer systems is because it can represent larger numbers using fewer digits compared to decimal.

So, how does hexadecimal representation relate to the number of cells in a computer's main memory? Well, the number of cells in memory is determined by the number of unique addresses that can be represented. In other words, each address can be thought of as a unique "location" in memory where data can be stored.

If each cell's address is represented by 2 hexadecimal digits, then there are 16 x 16 = 256 possible locations in memory. This means that there can be 256 cells in memory. Similarly, if 4 hexadecimal digits are used, there are 16 x 16 x 16 x 16 = 65536 possible locations, and therefore 65,536 cells in memory.

To address your question about the number of bits in each hexadecimal digit, it is important to understand that hexadecimal is simply a way to represent numbers, and does not directly relate to the number of bits. However, in computer systems, each hexadecimal digit is typically represented by 4 bits, also known as a "nibble". This means that a 2-digit hexadecimal number would be equivalent to 8 bits, and a 4-digit hexadecimal number would be equivalent to 16 bits.

In conclusion, the number of cells in a computer's main memory is determined by the number of unique addresses that can be represented. Using hexadecimal representation can allow for a larger number of addresses to be represented using fewer digits, making it a useful tool in computer systems.
 

1. How many cells are typically found in a computer's main memory?

The amount of cells in a computer's main memory can vary depending on the specific computer system. However, on average, a modern computer's main memory can hold billions or even trillions of cells.

2. What is the purpose of cells in a computer's main memory?

The cells in a computer's main memory are used to store data and instructions that the computer's processor can access and use for various tasks. This allows the computer to quickly retrieve and process information.

3. How does the amount of cells in a computer's main memory affect its performance?

The amount of cells in a computer's main memory can greatly impact its performance. Generally, the more cells a computer has in its main memory, the faster it can process and store data.

4. Is the amount of cells in a computer's main memory the same as its storage capacity?

No, the amount of cells in a computer's main memory is not the same as its storage capacity. Main memory is used for temporary storage of data and instructions while the computer is running, while storage capacity refers to the amount of data that can be permanently stored on the computer.

5. Can the amount of cells in a computer's main memory be upgraded?

Yes, the amount of cells in a computer's main memory can often be upgraded by adding more memory modules or replacing existing ones with higher capacity ones. This can improve the computer's performance and allow for more data to be stored in the main memory.

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