[mjk]: Binary clock is a clock representing time in binary coded decimals. This means that each value of the current time (hours, minutes, seconds) are extracted as an independent ten-based values (hours between 0-23, minutes and seconds between 0-59). Each of these values are treated as two digit values (so, for example, three minutes past five would be represented as: 05 03). To get a binary representation out of these values, each pair is chopped to single digits (0 5 0 3). Now each of these digits can be treated as a single 4-bit value and the time can be represented by using LEDs or some other kind of methods to show the state of the bits inside of these values.

Here's a small application I made for my own amusement:

[http://www.omanurkka.fi/files/binaryclock1.png]

======
 # Title:       Binary Clock
 # Author:      Matti J. Kärki
 # Date:        30.8.2004
 # Description: A small Tcl/Tk application showing current time in
 #              Binary Coded Decimal (BCD) format. This application
 #              requires the Img package.
 
 
 package require Tk
 package require Img
 
 # Background color for the window. Note that the color
 # "#0000AC" is the background color used in the images
 # representing the LEDs.
 set BGCOLOR     {#0000AC}
 
 # Base64 encoded image data for a non-lit LED (in BMP format).
 set OFFIMGDATA  {
     Qk3mAQAAAAAAADYAAAAoAAAADAAAAAwAAAABABgAAAAAALABAAAAAAAAAAAA
     AAAAAAAAAAAArAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA
     rAAArAAAAAAAAAAA/wAA/wAA/wAA/wAAAAAAAAAArAAArAAArAAAAAAA/wAA
     /wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAArAAArAAAAAAA/wAA/wAA/wAA/wAA
     /wAA/wAA/wAA/wAAAAAArAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA
     /wAA/wAAAAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAA
     AAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAAAAAA/wAA/wAA
     /////wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAArAAAAAAA/wAA/////////wAA
     /wAA/wAA/wAA/wAAAAAArAAArAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA
     /wAAAAAArAAArAAArAAAAAAAAAAA/wAA/wAA/wAA/wAAAAAAAAAArAAArAAA
     rAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA}
 
 # Base64 encoded image data for a lit LED (in BMP format).
 set ONIMGDATA   {
     Qk3mAQAAAAAAADYAAAAoAAAADAAAAAwAAAABABgAAAAAALABAAAAAAAAAAAA
     AAAAAAAAAAAArAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA
     rAAArAAAAAAAAAAAAAD/AAD/AAD/AAD/AAAAAAAArAAArAAArAAAAAAAAAD/
     AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAArAAArAAAAAAAAAD/AAD/AAD/AAD/
     AAD/AAD/AAD/AAD/AAAArAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/
     AAD/AAD/AAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAA
     AAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAAAAAAAAD/AAD/
     ////AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAArAAAAAAAAAD/////////AAD/
     AAD/AAD/AAD/AAD/AAAArAAArAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/
     AAD/AAAArAAArAAArAAAAAAAAAAAAAD/AAD/AAD/AAD/AAAAAAAArAAArAAA
     rAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA}
 
 set ONIMG   [image create photo -data $ONIMGDATA -format bmp]
 set OFFIMG  [image create photo -data $OFFIMGDATA -format bmp]
 set BITS    [list 1 2 4 8]
 
 # Returns a current time in {H H M M S S} format. The format is
 # suitable for representing the time in decimal or binary format.
 proc getBCDtime {} {
     set bcdtime {}
     set tim [split [clock format [clock seconds] -format {%H %M %S}]]
 
     foreach t $tim {
         set bcdtime [concat $bcdtime [split $t {}]]
     }
 
     return $bcdtime
 }
 
 # Updates the clock display every second. This function
 # scans through the return value of the getBCDtime function
 # and makes a bit-vise comparsion with the elements of the
 # BITS table.
 proc clocktick {} {
     set t [getBCDtime]
 
     for {set x 0} {$x < 6} {incr x} {
         for {set y 0} {$y < 4} {incr y} {
             set y1 [expr 3 - $y]
             if {[expr [lindex $t $x] & [lindex $::BITS $y]] == 0} then {
                 .lbl$x$y1 configure -image $::OFFIMG
             } else {
                 .lbl$x$y1 configure -image $::ONIMG
             }
         }
     }
 
     after 1000 clocktick
 }
 
 # Creates a GUI. Constructs a clock display by placing a set
 # of label widgets in grid. Labels are named by using the
 # co-ordinates of the widget and the prefix ".lbl".
 proc gui {} {
     . configure -background $::BGCOLOR
     for {set x 0} {$x < 6} {incr x} {
         for {set y 0} {$y < 4} {incr y} {
             label .lbl$x$y -image $::OFFIMG -background $::BGCOLOR
             grid .lbl$x$y -column $x -row $y
         }
     }
 }
 
 # Start the show...
 gui
 clocktick
======

----
[RHS] A friend of mine has a binary clock on his desk, and I've wondered ever since I first saw it... why have two columns for each number, with the first column being the tens? When not just do the whole number in binary (1,2,4,8,16,32 instead of 1,2,4,8,10,20,40)?

----
[mjk]: Good guestion, [RHS]. It's because of readability. For humans, who are accustomed to reading ten-based numbers, showing tens in different column is easier to interpret than trying to see the time from single binary representation.

Here's a modification, which displays time in three columns:

[http://www.omanurkka.fi/files/binaryclock2.png]

======
 # Title:       Binary Clock 2
 # Author:      Matti J. Kärki
 # Date:        30.8.2004
 # Description: A small Tcl/Tk application showing current time in
 #              Binary Coded format. This application requires
 #              the Img package.
 
 package require Tk
 package require Img
 
 set BGCOLOR     {#0000AC}
 
 set OFFIMGDATA  {
     Qk3mAQAAAAAAADYAAAAoAAAADAAAAAwAAAABABgAAAAAALABAAAAAAAAAAAA
     AAAAAAAAAAAArAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA
     rAAArAAAAAAAAAAA/wAA/wAA/wAA/wAAAAAAAAAArAAArAAArAAAAAAA/wAA
     /wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAArAAArAAAAAAA/wAA/wAA/wAA/wAA
     /wAA/wAA/wAA/wAAAAAArAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA
     /wAA/wAAAAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAA
     AAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAAAAAA/wAA/wAA
     /////wAA/wAA/wAA/wAA/wAA/wAA/wAAAAAArAAAAAAA/wAA/////////wAA
     /wAA/wAA/wAA/wAAAAAArAAArAAAAAAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA
     /wAAAAAArAAArAAArAAAAAAAAAAA/wAA/wAA/wAA/wAAAAAAAAAArAAArAAA
     rAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA}
 
 set ONIMGDATA   {
     Qk3mAQAAAAAAADYAAAAoAAAADAAAAAwAAAABABgAAAAAALABAAAAAAAAAAAA
     AAAAAAAAAAAArAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA
     rAAArAAAAAAAAAAAAAD/AAD/AAD/AAD/AAAAAAAArAAArAAArAAAAAAAAAD/
     AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAArAAArAAAAAAAAAD/AAD/AAD/AAD/
     AAD/AAD/AAD/AAD/AAAArAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/
     AAD/AAD/AAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAA
     AAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAAAAAAAAD/AAD/
     ////AAD/AAD/AAD/AAD/AAD/AAD/AAD/AAAArAAAAAAAAAD/////////AAD/
     AAD/AAD/AAD/AAD/AAAArAAArAAAAAAAAAD/AAD/AAD/AAD/AAD/AAD/AAD/
     AAD/AAAArAAArAAArAAAAAAAAAAAAAD/AAD/AAD/AAD/AAAAAAAArAAArAAA
     rAAArAAArAAArAAAAAAAAAAAAAAAAAAArAAArAAArAAArAAA}
 
 set ONIMG   [image create photo -data $ONIMGDATA -format bmp]
 set OFFIMG  [image create photo -data $OFFIMGDATA -format bmp]
 set BITS    [list 1 2 4 8 16 32]
 
 proc strip0 {num} {
     if {[regexp {^0([0-9]+)} $num -> num2] > 0} then {
         return $num2
     }
     return $num
 }
 
 proc getBCDtime {} {
     set bcdtime [split [clock format [clock seconds] -format {%H %M %S}]]
 
     return $bcdtime
 }
 
 proc clocktick {} {
     set t [getBCDtime]
 
     for {set x 0} {$x < 3} {incr x} {
         for {set y 0} {$y < 6} {incr y} {
             set y1 [expr 5 - $y]
             if {[expr [strip0 [lindex $t $x]] & [lindex $::BITS $y]] == 0} then {
                 .lbl$x$y1 configure -image $::OFFIMG
             } else {
                 .lbl$x$y1 configure -image $::ONIMG
             }
         }
     }
 
     after 1000 clocktick
 }
 
 proc gui {} {
     . configure -background $::BGCOLOR
     for {set x 0} {$x < 3} {incr x} {
         for {set y 0} {$y < 6} {incr y} {
             label .lbl$x$y -image $::OFFIMG -background $::BGCOLOR
             grid .lbl$x$y -column $x -row $y
         }
     }
 }
 
 gui
 clocktick
======

----
one might want to add that there already was a binary clock in the analog clock section [ALM]

----
[arezey], 8th January 2009: A simple binary clock in 42 lines of code.

======
 wm resizable . 0 0

 ttk::frame .fr
 grid .fr -row 0 -column 0

 set i 0
 foreach x {a b c d} {
         foreach y {1 2 3 4 5 6} {
                 canvas .fr.$x$y -background black -height 24 -width 24
                 grid .fr.$x$y -row $i -column [expr {$y-1}]
         }
         incr i
 }

 proc tick {} {
         foreach x {a b c d} {
                 foreach y {1 2 3 4 5 6} {
                         .fr.$x$y configure -background black
                 }
         }
         lassign [split [clock format [clock seconds] -format "%H:%M:%S"] ":"] h m s
         
         foreach e [list [list $h 1 2] [list $m 3 4] [list $s 5 6]] {
                 set c1 [lindex $e 1]
                 set c2 [lindex $e 2]
                 set v1 [string index [lindex $e 0] 0]
                 set v2 [string index [lindex $e 0] 1]
                 
                 if {$v1 >= 8} {.fr.a$c1 configure -background orange; incr v1 -8}
                 if {$v1 >= 4} {.fr.b$c1 configure -background orange; incr v1 -4}
                 if {$v1 >= 2} {.fr.c$c1 configure -background orange; incr v1 -2}
                 if {$v1 >= 1} {.fr.d$c1 configure -background orange}
                 if {$v2 >= 8} {.fr.a$c2 configure -background orange; incr v2 -8}
                 if {$v2 >= 4} {.fr.b$c2 configure -background orange; incr v2 -4}
                 if {$v2 >= 2} {.fr.c$c2 configure -background orange; incr v2 -2}
                 if {$v2 >= 1} {.fr.d$c2 configure -background orange}
         }
         
         after 1000 tick
 }

 tick
======

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