# The amount of cells in a computers main memory

1. Feb 17, 2010

### guitar

1. The problem statement, all variables and given/known data

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

2. Relevant equations

N/A

3. 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.

2. Feb 17, 2010

### Staff: Mentor

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. Feb 17, 2010

### guitar

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. Feb 17, 2010

### turin

I don't follow this. Each hex digit specifies four binary digits, so two hex digits specifies (two times four equals) eight binary digits.

Yes, there are sixteen possible values for each hex digit.