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I don't know if I asked the question in correct way but I will try to explain what's the thing I am not getting. I am currently reading book titled "Code: The Hidden Language of Computer Hardware and Software". In chapter sixteen, the book discusses structure of memory starting from latch. Following image shows 1 byte of memory where each bit is addressed by $s_0$, $s_1$ and $s_2$.

1 byte of memory

Above memory structure is reduced into the block diagram as show below.

Reduced Memory structure

Now, the book shows connecting two memory block. Now things got confusing for me from here.

Memory block connected together

Let us assume that both the memory block have some data in it. Now I would like to overwrite all the bits in $1st$ block of memory. So, I give signal to $A_0 , A_1$ and $A_2$ ranging from $000$ to $111$ while feeding $DI$ of the $1st$ block of memory. To write those data on our 1st block of RAM, I have to send write signal too. The write signal line and the address line both are connected to another block of memory too. Now when I send address and write signal, the second block of memory gets the signal too. But, I am not sending any data to second block of memory which essentially means 0 at Data In of second block. We assumed that the second block of memory also has some bit stored in it. When trying to write data on 1st block of memory, haven't I set all the bits in the second memory to zero? This wasn't what I wanted to do. How do I write in 1st block of memory without overwriting the data on second block of memory? Please enlighten me!

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You do write data in second block whenever you write data in 1st block of memory.
You can provide independent Data In to each block and expect it to be readable independently at the Data Outs: the second diagram depicts an 8 words of 2 bit memory.
The first one does not depict 1 byte of memory, but an 8 words of 1 bit memory.

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