Sequential circuits and memory

I read some books to understand why we need to memorise bits in electric circuits and found the sequential logic circuits are designed to achieve that goal.

The basic element is the SR Latch which can store one bit of information (0 or 1) and erase it. It is made of two cross-coupled NOR gates, that means many relays.

But we can achieve the same operation of memorising by using one relay: if the switch of the relay is closed the bit (1) is memorised and if it’s opened the bit is erased.

My questions are:

1. Why we use sequential circuits to memorize bits instead of simple relays?
2. Can the processor make arithmetic operations without using memory?
• Why do we use transistors instead of valves/tubes? Apr 23, 2020 at 16:03
• The transistor acts as a relay in digital circuits. Apr 23, 2020 at 16:41

"Sequential circuits" is an abstract idea. A Set-Reset latch made of cross-coupled NOR is just one example of a way to realize a sequential circuit. Could also be built from vacuum tubes or op-amps (with positive feedback and hysteresis) or some types of mechanical relays or even mechanical cogs and gears. Same basic design principles apply to all sequential circuits, regardless of the underlying technology. Technology changes. You're not studying a technology, you're studying the underlying design principles.

Arithmetic operations (such as unsigned 2's complement addition and subtraction) can be made from Combinational circuits (gates). Putting combinational circuits together with sequential circuits makes finite state machines, which lead to more complex machines like computers.

Abstract ideas are powerful but can be hard to grasp without a specific example, that's why your coursework is focusing on SR latch as a specific example of a simple sequential circuit element. It's something you could reasonably test in the lab and it's pretty close to what you will likely see in practice.

• So, you think the SR Latch is simpler for memorizing 1 bit than a single relay. Apr 24, 2020 at 19:32
• @u4783731 An SR latch is smaller, cheaper, uses less power, and is more reliable than an electromagnetic relay. So, yes, the SR latch is "simpler". Apr 25, 2020 at 14:05
• When I talk about the relay I meant the concept of the relay and not specially the electromagnetic one. The transistor acts as a relay in digital circuits, so smaller and cheaper than SR Latch. Apr 25, 2020 at 16:06

In combinational logic the output is a function of present input/output status.

In sequential logic the output is a function of both past and present input/output status. Thus sequential logic requires data storage (memory). How the data storage is done depends on the technology used (electromagnetic relays, magnetic memory, semiconductor memory etc.).

Basic arithmetic operations can be performed without using data storage.

• Note that "sequential" is a special case of "synchronous", in general synchronous logic does not need feedback...the present state can be unrelated to the previous state. Arithmetic operations can of course be performed without using data storage. Op amps do it all of the time, and combinational logic can do it without using feedback or storage. You are making invalid generalizations about these terms. Apr 25, 2020 at 14:06
• @Elliot Alderson, Thank you very much for your comments. My answer has been amended. Apr 25, 2020 at 14:15

Dynamic RAM uses a capacitor and a single transistor to store a bit. As you wonder, storing a bit does not require all of the transistors in two NOR gates. Your assumption that a SR latch was the simplest form of storage was not correct.

• Actually, it’s not my assumption. It’s what I found in all academic books about sequential circuits. The two cross-coupled NOR gates (SR Latch) is always introduced as the first basic component to store one bit of information. Apr 23, 2020 at 18:45
• But a dynamic RAM cell isn't really a memory circuit if it doesn't retain its state, and it doesn't provide the "memory" capability without a complex sense amplifier and precharge circuitry. We call it memory but it doesn't actually meet the formal requirements for a memory cell. The SR latch (or its functional equivalent) is the simplest form of a true memory circuit. Apr 25, 2020 at 14:02