Command to pad zeros to specific locations in binary numbers?

问题

I need to pad zeros to specific locations in binary numbers. Looping the array form of a binary number such as dec2bin(43) and adding the zeros and adjusting the size sounds reinvention of the wheel.

How to pad zeros efficiently to binary numbers in Matlab?

Looping

positions=[1,3,6];
x=de2bi(43);
xx=flip(x);    

kk=1;
for ii=1:length(x)+length(positions)
    if isequal(positions(kk),xx(ii))
         %Transfer the tail from ii by one index ahead,
         %left out here because I think my method is bad!
         x(ii)=0;
         positions=positions+1;  %Increase positions by one now due to one padding
         kk=kk+1;
    end
end

which feels too much reinvention: basically how to get 0 just before Y like from xxxxYabcd to xxxx0Yabcd where xxxxYabcd is a binary number?

Example

Input

101011, (1,3,6)

Output

100100110

1x010x11x (showing location of zeros clearer with x where zeros inserted)

回答1:

Although not much of a conceptual improvement, the following will do automatic re-indexing and assignment of the old values on a pre-padded matrix:

>> xx
xx =
     1     0     1     0     1     1

nPads = length(positions);
nPadsShifts = 1:nPads;           
y = ones(1, length(xx) + nPads); % re-indexing on the new array
y(positions + nPadsShifts) = 0;  % padding values
y(y==1) = xx;                    % set original bit values


>> y
y =
     1     0     0     1     0     0     1     1     0

回答2:

You can do it using just indexing. The positions of the zeros to be inserted in the extended vector are insertzeros+(1:length(insertzeros)) (where insertzeros is [1 3 6] in your example):

input = [1 0 1 0 1 1]; %// example data
insertzeros = [1 3 6]; %// example data

output = ones(1,length(input)+length(insertzeros));
output(insertzeros+(1:length(insertzeros))) = 0;
output(output==1) = input;

回答3:

Race begins! Mendo wins, gevang is a good second, thewaywewalk is the third and jaheruddin comes in fourth. The Shai's bitshifting is implemented in the shai function, unfortunately not yet getting it run faster.

Results

gevang :2.2e-05
thewaywewalk :5.6975e-05
mendo :2.2102e-05
jaheruddin :0.0001693
shai (poor hhh-implementation) 5.3288e-04

Warmed-up testing of the answers

function test_padding_zeros()

    function myOutput=gevang(xx,positions)
        nPads = length(positions);
        nPadsShifts = 1:nPads;
        myOutput = ones(1, length(xx) + nPads); % re-indexing on the new array
        myOutput(positions + nPadsShifts) = 0;  % padding values
        myOutput(myOutput==1) = xx;                    % set original bit values
    end

    function myOutput=thewaywewalk(x,positions)
        idx = numel(x):-1:1;
        myOutput = num2cell(x);
        myOutput(2,idx(positions)) = {0};
        myOutput = [myOutput{:}];
    end

    function myOutput=jaheruddin(myInput,positions) % myInput can be a row vector or a matrix!
        n = size(myInput,2)+numel(positions);
        myOutput = false(size(myInput,1),n);
        myOutput(:,setxor((1:length(positions)),1:n))=myInput;
    end

    function myOutput=mendo(myInput,positions)
        myOutput = ones(1,length(myInput)+length(positions));
        myOutput(positions+(1:length(positions))) = 0;
        myOutput(myOutput==1) = myInput;
    end

    function out = bizarreBitShift( bNum, fromBit, shiftAmount )
        % construct a mask
        msk = uint32( (2^( fromBit - 1 ) )-1 ); 
        shiftPart = bitand( uint32(bNum), bitcmp(msk) ); % bitcmp - complement of bits
        staticPart = bitand( uint32(bNum), msk );
        out = bitshift( shiftPart , shiftAmount );
        out = bitor( out, staticPart );
    end

    function myOutput=shai(myInput,positions)
        shiftAmount=1;
        myOutput=sprintf('%d',myInput);
        myOutput=bin2dec(myOutput);
        k=0;
        for ii=1:length(positions)
            fromBit=positions(ii)+k;
            myOutput=bizarreBitShift(myOutput, fromBit, shiftAmount);
            k=k+1;
        end

        myOutput=ismember(dec2bin(myOutput),'1');
    end




positions = [1 3 6]; %// example data
myInput = [1 0 1 0 1 1]; %// example data

ggevang=@() gevang(myInput,positions);
tthewaywewalk=@() thewaywewalk(myInput,positions);
mmendo=@() mendo(myInput,positions);
jjaheruddin=@() jaheruddin(myInput,positions);
sshai=@() shai(myInput,positions);

timeit(ggevang)
timeit(tthewaywewalk)
timeit(mmendo)
timeit(jjaheruddin)
timeit(sshai)

end

回答4:

If you are looking for efficiency it can never hurt to try various options. Here is another way to do it:

M = magic(5)>3; % Example matrix
positions = [2 3 6]; % Desired padding columns in resulting matrix

n = size(M,2)+numel(positions);
R = false(size(M,1),n);

R(:,setxor(positions,1:n))=M

回答5:

Shai provided here bitshifting solution for a single binary number. I use it below to pad the zeros, the solution can probably made far faster -- currently being one of the slowest solution (some unnecessary dec2bin) or about the same speed as Jaheruddin's solution.

function out = bizarreBitShift( bNum, fromBit, shiftAmount )
    % construct a mask
    msk = uint32( (2^( fromBit - 1 ) )-1 ); 
    shiftPart = bitand( uint32(bNum), bitcmp(msk) ); % bitcmp - complement of bits
    staticPart = bitand( uint32(bNum), msk );
    out = bitshift( shiftPart , shiftAmount );
    out = bitor( out, staticPart );
end

function myOutput=shai(myInput,positions)
    shiftAmount=1;
    myOutput=sprintf('%d',myInput);
    myOutput=bin2dec(myOutput);
    k=0;
    for ii=1:length(positions)
        fromBit=positions(ii)+k;
        myOutput=bizarreBitShift(myOutput, fromBit, shiftAmount);
        k=k+1;
    end

    myOutput=ismember(dec2bin(myOutput),'1');
end

positions = [1 3 6]; %// example data
myInput = [1 0 1 0 1 1]; %// example data

sshai=@() shai(myInput,positions);
timeit(sshai)

Timing

ans =

   5.3288e-04

来源：https://stackoverflow.com/questions/20791048/command-to-pad-zeros-to-specific-locations-in-binary-numbers