Before you can read the parent note, you need to know what each little symbol and word means and what it looks like. This page builds them one at a time, from nothing. If you have never seen a "bus", start here and read top to bottom.
We write them with a name and a small number below, like Master1 or Slave2. That little number is just a label to tell them apart — Master1 means "the first master", nothing more. In math this small low number is called a subscript.
How to read this figure: on the left the magenta box is Master1; on the right the violet box is Slave2. Follow the orange arrow going right — that is the master asking ("read address 42?"). Then follow the navy arrow coming back left — that is the slave replying ("here is the data"). The arrows never both start from the slave: a slave never speaks first. This one picture is the definition of a transaction — a question out, an answer back.
Why the topic needs this: the whole subject is "many masters, fewer roads, take turns." You cannot talk about taking turns until you know who is asking.
Look at the figure: three coloured wire-bundles, every device tapping onto the same bundle. That "tapping onto the same wire" is the source of every problem in this topic.
The parent note throws letters at you. Each is just a stand-in for a number you don't want to fix yet.
We use letters instead of numbers so one formula works for any size system. When you see B/N, read it out loud: "total road speed divided amongN masters" — each master's fair share.
Four tiny pieces of notation appear again and again. Learn to speak them.
Why the topic needs it (previewing a topology you'll meet later): one wiring shape in the parent note is the crossbar — imagine a grid of switches that lets several masters talk to several slaves at the same time, one independent path per pair (you'll study it in full in the parent note). With M masters and S slaves, a crossbar can run at most min(M,S) conversations at once — you can't have more simultaneous chats than you have masters or than you have slaves, so the limit is the smaller count.
Why the topic needs it: worst-case waiting time = add up every transaction Ti that jumps the queue ahead of you.
Why the topic needs it: round-robin arbitration hands the turn to master (i+1)modN — it circles back to master 0 after the last master, forever fair.
Read it top-down: you need devices and wires before topology; you need counting letters and math shorthand before you can read the arbitration formulas. Both streams meet at the parent topic.
Cover the right side and test yourself. If any answer surprises you, re-read its section above.
What is a master vs a slave?
The master starts a transaction (asks); the slave only answers when addressed.
What are the three wire-groups of a classic bus?
Address lines, data lines, control lines.
Why can only one transaction use a shared bus at a time?
Two devices driving the same wire cause an electrical collision — the wire can't show two values at once.
Do M and N mean different things?
No — both mean "number of masters"; N is used in arbitration formulas, M in crossbar formulas.
Read B/N in words.
Total bus bandwidth divided evenly among N masters — each master's fair share.
What does min(M,S) give and why does the topic use it?
The smaller of M and S; a crossbar can't run more simultaneous conversations than it has masters or slaves.
What does Ti stand for in the sum?
The time master i's transaction takes (how long it holds the bus).
Expand ∑i=02Ti.
T0+T1+T2.
Compute (2+1)mod3 and say what it models.
0; the round-robin turn wrapping from the last master back to master 0.
What does ni mean in the bandwidth formula?
The number of time-slots owned by master i in the repeating TDM schedule.
If master i owns 2 of 8 TDM slots, what fraction of bandwidth does it get?
2/8=25%.
Define topology and arbitration in one phrase each.
Topology = the shape of the wiring; arbitration = the rule that picks a winner among competing masters.
Recall Self-check: could you draw a shared bus with 3 masters from memory?
You should be able to draw three master boxes all tapping onto one address+data+control bundle, and explain that only one may drive the data wires at a time. If yes, you are ready for the parent note.
