Editing Counter (digital) (section)

===Johnson counter===

A [[Johnson counter]] is a circular shift register in which the output of the last stage is inverted and connected to the data input of the first stage,<ref>{{cite book | title = Digital Principles Foundation of Circuit Design and Application | first = Arun Kumar | last = Singh | publisher =  New Age Publishers | year = 2006 | isbn = 81-224-1759-0 | url = https://books.google.com/books?id=13Wi37h2A-oC&q=switchtail+ring+counter+johnson&pg=PA113}}</ref><ref>{{cite book | title = The Art of Electronics | first1 = Paul | last1 = Horowitz | first2 = Winfield | last2 = Hill | publisher = Cambridge University Press | year = 1989 | isbn = 0-521-37095-7 | url = https://books.google.com/books?id=bkOMDgwFA28C&q=ring+counter+walking&pg=PA667}}</ref><ref>{{cite book | title = Modern Dictionary of Electronics | first = Rudolf F | last = Graf | publisher = Newnes | year = 1999 | isbn = 0-7506-9866-7 | url = https://books.google.com/books?id=uah1PkxWeKYC&q=moebius+ring+counter+johnson&pg=PA401}}</ref> and all bits are initialized to zero, thus producing a [[Gray code]] output sequence. It can be clocked at relatively high frequencies because there are no intermediate logic gates, and consequently the worst-case propagation delay is from clock to flip-flop output. A Johnson counter is MOD-2n, where n is the number of flip-flops. For example, the Johnson counter shown below has four flip-flops and therefore is a MOD-8 counter.

[[File:Johnson Counter 4bit.svg|400px|border|4-bit Johnson counter using four [[Flip-flop (electronics)#D flip-flop|D-type flip flops]]]]

{|class="wikitable" style="text-align:center"
|-
! colspan="5"|4-bit Johnson counter output states
|-
! | State || Q0 || Q1 || Q2 || Q3
|-
! 0
| 0 || 0 || 0 || 0
|-
! 1
| style="background:#0FF"|1 || 0 || 0 || 0
|-
! 2
| style="background:#0FF"|1 || style="background:#0FF"|1 || 0 || 0
|-
! 3
| style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || 0
|-
! 4
| style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1
|-
! 5
| 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1
|-
! 6
| 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1
|-
! 7
| 0 || 0 || 0 || style="background:#0FF"|1
|}

Johnson counters are commonly used in state machines and in specialized applications such as analog waveform generation (e.g., Davies sinusoidal generator).<ref name="davies">{{cite web |last1=Dunbar |first1=Steven |title=The Davies Sinusoidal Generator |url=https://www.ti.com/lit/an/sboa550/sboa550.pdf |publisher=Texas Instruments |access-date=27 March 2025}}</ref>