A recent query on comp.lang.tcl asked how one might find the sum of two binary numbers, without converting them to decimal returning the result as binary.

[Glen Jackson] wrote the following code:

======
    if {[string match 8.4* [package require Tcl]]} { 
	package require struct::list 
	interp alias {} list_reverse {} struct::list reverse 
    } else { 
	interp alias {} list_reverse {} lreverse 
    } 


    proc add_binary_strings {n1 n2} { 
	set answer [list] 
	set carry 0 
	foreach d1 [list_reverse [split $n1 ""]] \ 
		d2 [list_reverse [split $n2 ""]] \ 
	{ 
	    if {$d1 eq ""} {set d1 0} 
	    if {$d2 eq ""} {set d2 0} 
	    switch -exact [set sum [expr {$d1 + $d2 + $carry}]] { 
		0 - 
		1 { set carry 0 } 
		2 { set sum 0; set carry 1 } 
		3 { set sum 1; set carry 1 } 
	    } 
	    lappend answer $sum 
	} 
	lappend answer $carry 
	return [string trimleft [join [list_reverse $answer] ""] 0] 
    } 


    set n1 100010111 
    set n2   1011011 


    puts "$n1 + $n2 = [add_binary_strings $n1 $n2]" 

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[Lars H]: Ah, but it's slightly neater to do it without [expr]:
    proc add_binary_strings {n1 n2} { 
	set sum {}
	set carry 0 
	foreach d1 [list_reverse [split $n1 ""]] d2 [list_reverse [split $n2 ""]] { 
	    switch -- [string map {0 ""} "$d1$d2$carry"] { 
		""  { lappend sum 0; set carry 0}
		1   { lappend sum 1; set carry 0}
		11  { lappend sum 0; set carry 1}
		111 { lappend sum 1; set carry 1}
	    } 
	} 
	lappend sum $carry 
	return [string trimleft [join [list_reverse $sum] ""] 0] 
    } 


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See also:
   * [Binary representation of numbers]

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%| [Category Mathematics] | [Category Binary Data] |%
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