Let’s build a stack!

STACKS

• Random access memory requires knowing the address of every byte/word you want to access
• Hardware stacks created out of dedicated shift registers
• So let’s build one!

LET'S BUILD A STACK...

• Start with a bi-directional shift register...
• Start off with 4 D flip-flops:
• ADD THE STANDARD SIGNALS
• Clock
• CLR (resets flip flops when up in Logisim)

ADD THE SERIAL INPUT (D)

• Data is the serial input (SI)

CONNECT EACH Q OUTPUT TO THE NEXT DATA INPUT

ADD SOME LEDS TO SEE THE PARALLEL OUTPUT / REGISTER

STATE

• We can now modulate the Data input and see the on state propagate through the register (left to right).

THIS CIRCUIT WILL DO MOST THINGS WE NEED:

• To get serial out, record the state of the right-most LED.
• To get parallel out, feed each LED into a register (latch) and stop the clock when the conversion is complete.
• To do parallel input, OR each D input with the state of a register and start the clock.

but it won't go backwards...

HOW DO WE MAKE IT GO BACKWARDS?

• Wire-up the cascade backwards
• Data goes in the far end, each Q outputs to the D input of the previous Flip-Flop.

HOW DO WE MAKE THE DIRECTION SELECTABLE?

• Remember those controlled logic gates in Week 2?

Select this

AND gate (Ci low)

OR gate (Ci high)

HOW DO WE MAKE THE DIRECTION SELECTABLE?

• More specifically, we need to determine from which direction each Flip Flop will receive its input.

• A controlled gate (remember Week 2!).

PROGRAMMABLE WIRING

• We can use one of these circuits for each input to a Flip- Flop, and use a common control signal to determine direction.

A, B' Output

1 A 0 B

SELECTING THE OUTPUT WITH GATES

• We also need to determine which direction output from a Flip Flop flows!
• This circuit has a common input, and selectable output.
• We can use one of these for each output from a Flip-Flop, and use a common control signal to determine direction.

A, B' Input

1 A

0 B

LET'S PUT THIS ALL TOGETHER

(JUST 2 FFS TO START WITH)

ADD THE GATES FOR SETTING INPUT

SELECT INPUT

ADD THE OUTPUT DIRECTION SELECTION

• R circuit enabled (red)

in out

Input D

Q D

OTHER DIRECTION SELECTED?

in out

Input D

Q D

WHAT COULD POSSIBLY GO WRONG?

• Can't short the outputs of two gates together.
• Have to Add with an OR gate.

in out

Conflict

THE FIX

• The OR gates combine the outputs of the controlling AND gates and pass through the signal from whichever one is enabled... to the D inputs on each Flip-Flop.

in ff 1 ff 2 out

in out

Generally need about 3 gates per flip-flop per bit

NEED MORE DEPTH?

• This is a 4-deep shift register (

http://www.ee.usyd.edu.au/tutorials/digital_tutorial/part2/ register06.html).

• As you can see, there are alternative ways of wiring it up, with different logic gates.

TO MAKE A STACK...

• So far we have made a 2-stage bi-directional 1-bit shift register.
• To make a proper stack:
• Add depth (flip-flops with associated control logic)
• Add width (bits) in parallel (common clock, control signals).
• identical shift-registers – one for each bit.

SUMMARY

• Hardware stacks formed using banks of shift registers
• Simple input selective circuits allow direction selectability:
• Programmable gates!
• To make a proper stack:
• Add depth (flip-flops with associated control logic)
• Add width (bits) in parallel (common clock, control signals).
• identical shift-registers – one for each bit.