From c5394b786404a2c92ea56179ec8bc24ffb548483 Mon Sep 17 00:00:00 2001 From: Spencer Date: Thu, 22 Feb 2024 11:27:35 +0900 Subject: [PATCH] auto commit via obsidian-git: 2024-02-22 11:27:35 Affected files: content/A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count.md content/attachments/Screenshot 2024-02-22 at 10.53.13 AM.png content/attachments/Screenshot 2024-02-22 at 11.03.37 AM.png --- ...with a toggling top-bit every 5th count.md | 32 ++++++++++++++++++ .../Screenshot 2024-02-22 at 10.53.13 AM.png | Bin 0 -> 946974 bytes .../Screenshot 2024-02-22 at 11.03.37 AM.png | Bin 0 -> 849044 bytes 3 files changed, 32 insertions(+) create mode 100644 content/A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count.md create mode 100644 content/attachments/Screenshot 2024-02-22 at 10.53.13 AM.png create mode 100644 content/attachments/Screenshot 2024-02-22 at 11.03.37 AM.png diff --git a/content/A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count.md b/content/A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count.md new file mode 100644 index 0000000000000..18857cf4fd667 --- /dev/null +++ b/content/A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count.md @@ -0,0 +1,32 @@ +--- +title: A biquinary counter is a mod-5 counter with a toggling top-bit every 5th count +date: 2024-02-22 +description: +tags: + - electronics +slug: +draft: false +math: false +--- + +biquinary +**:** of, based on, being, or relating to a mixed-base system of numbers in which each decimal digit _n_ is represented as a pair of digits _xy_ where _n_ = 5_x_ + _y_ and _x_ is written in base 2 (binary) as 0 or 1 and _y_ is written in base 5 (quinary) as 0, 1, 2, 3, or 4 + +It is a count-to-5 3-bit counter with a 4th top bit toggling every 5th count (so two cycles of 5 counts). + +When using the 74LS90 BCD decade counter for the first time I was wondering why they had two separate counters in side, a mod-2 counter and a mod-5 counter. + +The common way to configure the 74LS90 as a BCD 4-bit decade counter is as follows ([source](https://www.uobabylon.edu.iq/eprints/publication_12_16297_163.pdf)- CLK A is the mod-2 counter input and CLK B is the mod-5 counter input): +![](attachments/Screenshot%202024-02-22%20at%2010.53.13%20AM.png) +_By connecting, `Q_A`, the output of the mod-2 counter (1-bit output that toggles every two cycles) to, `CLK_B`, the input of the mod-5 counter (3 bit output that counts up to 5), we create a mod-10 (decade) counter._ + +But we can also create a _biquinary_ counter, where for the 4 bit output the bottom 3 bits have two cycles of incrementing from `000...100`, and the MSB is `0` for the first 5 sub-cycles, and `1` for the last 5. A timing and state diagram explains it better: +![](attachments/Screenshot%202024-02-22%20at%2011.03.37%20AM.png) +_Note clocks are falling edge triggered. The way to setup the biquinary counter is to have the main clock input into `CLK B` (the mod-5 counter) and have the `Q_D` output (MSB of the mod-5 counter) as the input to `CLK A`. This means when the mod-5 MSB goes from `1`→`0` (on the 5th count) the mod-2 counter will toggle. Note that the biquinary outputs must be taken as shown, with `Q_A` as the MSB and `Q_B` as the LSB._ + +**Usefulness** +The top bit can be thought of as a checksum .This is actually used in the Japanese abacus counting system. It seems it is also used in one of the worlds oldest existing working computers [([hackaday](https://hackaday.com/2019/08/03/maybe-the-oldest-computer-probably-the-oddest/))], but here it is implemented with 7 relays for 7 bits, instead of the 4 bits above . + +#todo add photo of abacus + +#todo add project link diff --git a/content/attachments/Screenshot 2024-02-22 at 10.53.13 AM.png b/content/attachments/Screenshot 2024-02-22 at 10.53.13 AM.png new file mode 100644 index 0000000000000000000000000000000000000000..09b27f143de6a692842bc35c40aa595731d44c3e GIT binary patch literal 946974 zcmZ^L1z4NEw=nLuu?@Ge!NzcR-G&TzFANG4C|0bv4cTya84QNI+mPW>T#CC(@nRpp z|JCQa_vU%hocH8Na+1DD&Pf}lsw_*0M~R1mfyc$f(N8$k3}g*;{~YfhZ_)VF^0ex*GkjG7Vy*C9O~~@`9EyP~W5G1;NndI07P~ zF>v1YNRm|M{=h3U`uHcf?E5=c$%D|0PZd|6o?!xwSZ5Oi-e>Q(AzIJ8A;-RtLT6b# z+aqk~e)I1m<>DiX(4!fLNP97ECwiIRPRNU)pnjIbpGET|642=m|Bic{QAmEZ%$E@IQCHvyo zM6Dz5SVVmschmj1g5C~QQvO@lvjX(&c_OHXxB!jy?@O73cN@4tD8I)TF8lja1_A{! 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