Address Space -- How many addresses are possible?

Addressability -- How big is each memory location

• If you have a memory with a 16-bit address in which each byte is given a distinct memory address, the addressability of the memory this memory is 8 bit.

• If you have a memory with a 16-bit address in which each byte is given a distinct memory address, the address space of this memory is $2^{16}=65536$

Basic building block of a memory

• Register
  • Gated D Latch

• Decoder

• Multiplexors

• A $2^3*3$-bit Word Memory

  

Edge-triggered(Leader-Follow) Flip Flop

Edge-triggering: The circuit’s data inputs have control only during the time that the enable input is transitioning from one state to another. (It is desirable to limit the responsiveness of a latch circuit to a very short period of time instead of the entire duration that the enabling input is activated.)

• Positive Edge-trigger

  

• Negative Edge-trigger

  

Full circuit:

Questions & Answers

If you have a memory with a 16-bit address in which each byte is given a distinct memory address, what is the addressability of this memory?

8 bits

If you have a memory with a 16-bit address in which each byte is given a distinct memory address, what is this memory’s address space?

$2^{16}=$ 65536

What is the difference between address space and addressability?

Computer memory is made up of distinct memory addresses, each containing some amount of data

• Address space: the number of memory addresses that exist

• Addressability: the amount of data stored at any given memory address
  • An n-bit address line can represent 2n memory addresses

What are the address space and addressability if

• A memory address is 13 bits, and there are 16 bits of data at each memory address?
  • Address space: $2^{13}$
  • Addressability: 16 bits

• There are 1024 memory addresses and the memory is byte-addressable?
  • Address space: 1024
  • Addressability: 8 bits

• There are 2048 memory addresses and the memory is 8KiB (8⨯1024⨯8 bits) in total?
  • Address space : 2048
  • Addressability : 65536 / 2048 = 32 bits

• A memory unit has 4KiB (4⨯1024⨯8 bits) of total storage and every bit has its own address?
  • Address space: 4x1024x8
  • Addressability: 1 bit since every bit has its own address

• The "address" input of a memory unit is 16 bits wide and the "data" input of the memory unit is 32 bits wide?
  • Address space: $2^{16}$
  • Addressability: 32