** See Also ** [Bit Manipulations]: [http://wiki.tcl.tk/8492#pagetoc9f073a72%|%Iterate over an IP address Range], by [kbk]: [SierpiƄski triangle]: A simple bit manipulation plays a role in a clever solution to a particular problem. ** 1-Bits in a positive int ** count the number of bits of value 1 in an integer (sign-extended for negatives, so better use positives only): ====== proc nbits n { set f [format %X $n] set res 0 foreach nybble {0 1 2 3 4 5 6 7 8 9 A B C D E F} \ bits {0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4} { set res [expr $res+$bits*[regsub -all $nybble $f - -]] } set res } ;# RS ====== More than 30 times faster, and works for negative numbers too: ====== proc popcount { i } { # count the population of ones in the integer i set pop 0 while { $i != 0 } { incr pop set i [expr { $i & ( $i - 1 ) }] } return $pop } ;# kbk [http://titania.crd.ge.com/people/kennykb.html] ====== This one is slower than the last, but it's a one-liner: ====== proc nbits2 n { expr 0[string map {0 +0 1 +1 2 +1 3 +2 4 +1 5 +2 6 +2 7 +3 8 +1 9 +2 A +2 B +3 C +2 D +3 E +3 F +4} [format %X $n]] } ====== For me, popcount freezes with negative numbers and popcount seems to be wrong for larger numbers ( like 12345678901234567890 ). Here's my one-liner, only slightly slower than popcount and shorter than nbits2. (chiligrower 20150708) ====== proc bcnt n { string length [ string map {0 ""} [ format %b $n ] ] } ====== <> Binary Data