This document proposes a new definition of "broad-sense synchronous circuits" that generalizes conventional definitions. Broad-sense synchronous circuits are defined as those with an order-preserving referential map, which determines the time points a circuit can refer to in its feedback. This definition includes traditionally synchronous circuits using flip-flops but does not require them, and excludes memory-equipped circuits that can refer to arbitrary past times. The proposed definition aims to locate an appropriate level of generality between existing too-narrow and too-broad definitions of synchronous circuits.

1. 1
Broad-sense Synchronous Circuits
on Partially Ordered Time
2016.12.08 ICAST
Shunji Nishimura

2. Introduction [1/5]
<existing1> : Synchronous circuits
= with D-FF(Flip-Flop) at feedback-loops :
combinational
circuit
D-FF
input output
state-out
clock
state-in
⇒ widely used and equivalent to state machines
2

3. Introduction [2/5]
<existing1> : Synchronous circuits
= with D-FF(Flip-Flop) at feedback-loops :
⇒ widely used and equivalent to state machines
3
D-FF
i
o
clk
D-FF
D-FF
i
o
clk
=
combinational circuit

4. Introduction [3/5]
 From the point of view of “circuit classes”
This <existing1> definition seems too narrow
to be a general circuit class because it employs
the particular element: D-FF.
(What is so special about D-FFs?)
 There is an another definition:
<existing2> : synchronous means that state transitions
are controlled by some signals.
4

5. Introduction [4/5]
Consider a circuit with a memory at the feedback-loop.
This matches <existing2>. But is it OK to call this synchronous...?
Theoretically, it can refer to any past states on demand, and so
it almost describes a general sequential circuit.
⇒ We don’t call it synchronous.
memory
write
control, address
read
combinational
circuit
input output
state-outstate-in
5

6. Introduction - summary
 Definition by D-FFs <existing1> ⇒ too narrow
Controlled by some signals <existing2> ⇒ overbroad
 want to find a new definition between these.
This study provides a new definition called
“broad-sense synchronous,” and this
locates between the existing two definitions.
6

7. Pre-structural Model [1/2]
 Conventional circuit model
 Pre-structural circuit model
f
input output
state-out
time t0
fstate-in
time t1
feedback-delay
input output
f
input output
state-out
time ta
fstate-in
time tb
time ordering
input output
refers to the last time
refers to a past 7

8. refers to the left
Pre-structural Model [2/2]
 Pre-structural circuit can refer to a past that is
not necessarily the last time.
 A D-FF synchronized cicuit refers to as below:
f f f
latched state
clock
refers to the left
8

9. Investigation of Referential Maps [1/4]
f
 use a map r (called referential map) to
determine destinations to refer.
f f
t0 t1 t2
r(t1)= t0
r(t2)= t0
 r : time → time 9

10. Investigation of Referential Maps [2/4]
 D-FF synchronized
clock
 serial D-FF synchronized
clock
: referential map
combinational
circuit
D-FF D-FF
input output
state-out
clock
state-in
combinational
circuit
D-FF
input output
state-out
clock
state-in
10

11. Investigation of Referential Maps [3/4]
 memory-equipped circuit
t0 t1
control signals
read a state
at t1
write
the state
write
the state
t2 t3
read a state
at t0
11
memory
writeread
combinational
circuit
input output
state-outstate-in
control signals

12. Investigation of Referential Maps [4/4]
 List of referential maps :
memory-equipped
： time ordering
： referential maps
D-FF synchronized
serial D-FF
synchronized
order-
preserving
not order-
preserving
12

13. Proposal / Validity
 Proposal：
has an order-preserving referential map
= broad-sense synchronous
 Validity：
1. includes conventional synchronous
⇒ broader concept
2. doesn’t employ any particular element
⇒ not too narrow
3. doesn‘t include memory-equipped
⇒ not overbroad
13