First, I have to assume some things, as your description of the problem is quite general: I believe, that you want to use a RAM chip to convert Binary to Gray code. And I am basing my comments and advice to that assumption. Sounds that you have first learn some basics regarding static RAM chips.
I am using 74LS89 as the example here, but very similar facts apply to all static RAM chips. If you want to become a designer of digital electronics, pay attention, behavior of static RAM chips is absolutely fundamental - 74LS89 is one of the absolutely simplest devices in that class, so it is a good device to learn the basic rules!
Briefly, they can be either "enabled" or "disabled" - depending on a line called /CS. A low value on /CS "enables" the chip. If /CS is high, the chip does not do anything at all, if /CS is low, it can be "read" or "written to". Writing is controlled by line /WE: When that line pulses down while /CS is also low, the data presented at chip input lines D1...D4 is stored in the memory, to the location selected by lines A0...A3.
In general, one must make sure, that binary value on A0...A3 is stable the whole time /CS and /WE are both low. Otherwise the result is unpredictable! However, when /CS is low, and /WE is held high, the data value stored in the memory will be visible on output lines O1...O3. In that situations the address lines may change state without too dramatic consequences, the output line state only changes to represent the (new) addressed location.
First: I have not checked the particular initial state of 74LS89 after power-on, but one thing is for sure: It is nothing useful in this context. So you have to write the conversion table in it during system initialization (that is, at least after every power off->on transition). That applies to (nearly) all RAM chips: The content is undefined at power-on.
Code conversion is in general done by storing a content in memory so that when input code (Binary here) is connected to the address lines, then one can read out the desired value (Gray code here) from that address.
To use a RAM device as such converter, the conversion table (=correct Gray code value for each binary input value) must be written into the memory. After such initialization the conversion works while the memory is in read mode: Each time an input value is presented to the address lines, desired converted value is visible at the data output lines. (/WE held high, and /CS is held low)
74LS89 has separate data in and data out lines, which makes the initialization circuit quite straight forward. I assume that a processor system, such as a microcontroller, is used to initialize the system. The data-in lines (D1...D4) are used by the processor to write the RAM chip contents.
During initialization, then, the processor has to write the ram by presenting all value from 0000 to 1111 - one value for writing each location - to the address lines of the 74LS89 chip, while at the same time presenting correct Gray code value on lines D1...D4, and executing a write cycle (/CS line pulsed or held low, while pulsing /WE line low).
During conversion phase, then, the binary value is presented to the address lines, the /CE is held low (while /WE is held high), and the converted value is presented on lines O1...O4.
The practical wiring depends very much about other requirements on the system level, so it is impossible to advice about deeper details, based on the facts you had in your question.
Good luck!