user31105: Background:
A few days ago I received a 23LC1024 1Mbit SRAM chip, which works like a charm.
However, before I ordered that one, I ordered a LP621024D-70LL which also is a 1 Mbit SRAM but in DIP32 format, meaning LOTS of pins.
Now I made a breadboard setup with 3 shift registers 74HC595 to be able to set the address (tested with LEDs but should work).
However, when trying use a shift register for the data which can be read or write, I don't think I can use a 74HC595 since it is only for output. However, I also don't think a 74HC165 (shift in register) would work (if I had one).
Questions:

What kind of shift register would I need, one that can do both input and output? I read about I2C registers but that seems to be a bit of overkill.
I only have 74HC595 shift registers for setting the address, would that slow down SRAM? I mean are there faster registers? Not that I want to buy it, but just curious. 

Here is a picture of a working LP621024D-70LL ... too bad the chip is barely visible , on the left are 2 74HC595s and right are also 2 (right one not used), these 3 shift registers take care of the address (17 bits -> 3 bytes). The SRAM itself is hidden under the center of the cables.


user10794: From the web page about the 23LC1024:

The memory is accessed via a simple Serial Peripheral Interface (SPI) compatible serial bus.

Using the SPI hardware on your Uno will be a lot faster than using software-based shifting. See my page about SPI.

user31038: since you already have input, use an 74HC165  8-bit parallel-in/serial out shift register. They are cheap.
another cheap option with I/O is an expander like the PCF8574, which are almost cheap

31105: <p>Background:</p>

<p>A few days ago I received a 23LC1024 1Mbit SRAM chip, which works like a charm.
However, before I ordered that one, I ordered a LP621024D-70LL which also is a 1 Mbit SRAM but in DIP32 format, meaning LOTS of pins.</p>

<p>Now I made a breadboard setup with 3 shift registers 74HC595 to be able to set the address (tested with LEDs but should work).</p>

<p>However, when trying use a shift register for the data which can be read or write, I don't think I can use a 74HC595 since it is only for output. However, I also don't think a 74HC165 (shift in register) would work (if I had one).</p>

<p>Questions:</p>

<ol>
<li><p>What kind of shift register would I need, one that can do both input and output? I read about I2C registers but that seems to be a bit of overkill.</p></li>
<li><p>I only have 74HC595 shift registers for setting the address, would that slow down SRAM? I mean are there faster registers? Not that I want to buy it, but just curious. </p></li>
</ol>

<p>Here is a picture of a working LP621024D-70LL ... too bad the chip is barely visible , on the left are 2 74HC595s and right are also 2 (right one not used), these 3 shift registers take care of the address (17 bits -> 3 bytes). The SRAM itself is hidden under the center of the cables.</p>

<p><a href="https://i.stack.imgur.com/w0M2E.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/w0M2E.jpg" alt="enter image description here"></a></p>
 10794: <p>From the <a href="http://www.microchip.com/wwwproducts/en/23LC1024" rel="nofollow noreferrer">web page about the 23LC1024</a>:</p>

<blockquote>
  <p>The memory is accessed via a simple Serial Peripheral Interface (SPI) compatible serial bus.</p>
</blockquote>

<p>Using the SPI hardware on your Uno will be a <em>lot</em> faster than using software-based shifting. See <a href="http://www.gammon.com.au/spi" rel="nofollow noreferrer">my page about SPI</a>.</p>
 31038: <p>since you already have input, use an <a href="http://assets.nexperia.com/documents/data-sheet/74HC_HCT165.pdf" rel="nofollow noreferrer">74HC165</a>  8-bit parallel-in/serial out shift register. They are <a href="http://www.ebay.com/itm/141975802074" rel="nofollow noreferrer">cheap</a>.</p>

<p>another cheap option with I/O is an expander like the <a href="http://www.ti.com/lit/ds/symlink/pcf8574.pdf" rel="nofollow noreferrer">PCF8574</a>, which are <a href="http://www.ebay.com/itm/141975859541" rel="nofollow noreferrer">almost cheap</a></p>
