Where do I truncate the bits in SHA 256 hash algorithm?

Question

I'm implementing SHA-256 in PHP using strings. Where do you truncate in the algorithm?

There are a lot of places where there's binary addition happening so the number of bits in $W(i)$ keep increasing. Same case with the compression function. So, where do I truncate the values?

When I var_dump my array I get this:

array(64) { 
[ 0]=> string(32) "01100001001000000111010001100101"
[ 1]=> string(32) "01110011011101001000000000000000" 
[ 2]=> string(32) "00000000000000000000000000000000" 
[ 3]=> string(32) "00000000000000000000000000000000" 
[ 4]=> string(32) "00000000000000000000000000000000" 
[ 5]=> string(32) "00000000000000000000000000000000" 
[ 6]=> string(32) "00000000000000000000000000000000" 
[ 7]=> string(32) "00000000000000000000000000000000" 
[ 8]=> string(32) "00000000000000000000000000000000" 
[ 9]=> string(32) "00000000000000000000000000000000" 
[10]=> string(32) "00000000000000000000000000000000" 
[11]=> string(32) "00000000000000000000000000000000" 
[12]=> string(32) "00000000000000000000000000000000" 
[13]=> string(32) "00000000000000000000000000000000" 
[14]=> string(32) "00000000000000000000000000000000" 
[15]=> string(32) "00000000000000000000000000110000" 
[16]=> string(32) "10001111101010001101101001000010" 
[17]=> string(32) "01110011100100101000000000000000" 
[18]=> string(32) "01110110010010101111110000010111" 
[19]=> string(32) "00010000000111001101001100011011" 
[20]=> string(32) "00100001100101001100011101010011" 
[21]=> string(32) "11110011111010101110110100111001" 
[22]=> string(32) "11111011010010111001000111111001" 
[23]=> string(32) "10111010101100000001011101110101" 
[24]=> string(33) "100101110100011111001000000101000" 
[25]=> string(32) "01111111110001011100001000100010" 
[26]=> string(33) "010000100100001011110010010001101" 
[27]=> string(32) "01111010110111110100100010111101" 
[28]=> string(33) "110010001011110100010000011100100" 
[29]=> string(33) "101001000101000110011011111011111" 
[30]=> string(33) "111000011011101011011101110010101" 
[31]=> string(34) "1111001011100001001101111011110110" 
[32]=> string(34) "1010010011000001000100101100000010" 
[33]=> string(35) "10101101001100111001111100111111010" 
[34]=> string(34) "1110100101001100001000011110000110" 
[35]=> string(36) "100101010100100001101110101111000011" 
[36]=> string(34) "1110001101001101001101110111011000" 
[37]=> string(36) "110101001100000100001110011000000101" 
[38]=> string(36) "100110010110100011010111011101100110" 
[39]=> string(36) "101110011100110000110001010010110000" 
[40]=> string(36) "100000101011010110001001000100011101" 
[41]=> string(37) "1001110001010110110001110110101011101" 
[42]=> string(37) "1000000101001011010111010000001100100" 
[43]=> string(37) "1001000011101111000001111110010100100" 
[44]=> string(38) "10010000101101110001100100010100010101" 
[45]=> string(37) "1011111001101101011111001000110010000" 
[46]=> string(39) "100101011110011011000000001001110010001" 
[47]=> string(37) "1001101011101110111000000100111010000" 
[48]=> string(39) "010001011100001101101000011010011100010" 
[49]=> string(38) "10011100010110000011111110010101101000" 
[50]=> string(39) "110011100111000010101100100101110011001" 
[51]=> string(38) "11001101111101010001000010110001100100" 
[52]=> string(40) "1001010000101100000100110100110000100011" 
[53]=> string(40) "1000010101011111001110000100101100111000" 
[54]=> string(40) "1111011111011011100000000001110000011101" 
[55]=> string(40) "0101110001001001110010001011110111010010" 
[56]=> string(40) "0100111101101110101111101011110000000011" 
[57]=> string(40) "1100101000101110000000101100000111111110" 
[58]=> string(40) "1101100110111011011010010001101100000100" 
[59]=> string(41) "10000100101011000111001100110101010010001" 
[60]=> string(41) "10111001010111100010000110001111101100110" 
[61]=> string(42) "110001101011011010100110111110101100101111" 
[62]=> string(42) "101001011000100100011001011101100100101111" 
[63]=> string(42) "101110011001100001001100001010110101001111" 
} 

Do I truncate the values before pushing them to the array or after the array is done with? If I truncate before, corresponding iterations will take up truncated values and that changes their values.

Also

$tmp=$q4;
$tr1=substr($tmp,-32);

$tmp2=binary_add($s0,$maj);
    $tr2=substr($tmp2,-32);

$H=$G;
$G=$F;
$F=$E;
$E=binary_add($tr1,$D);
    $D=$C;
    $C=$B;
    $B=$A;
    $A=binary_add($tr1,$tr2);

here too notice that I have truncated before adding the temp variables (and updating the var A to H) is this correct? Please let me know if I need to upload the whole code.

I am implementing this because this is my assignment.I have been getting different values and I am pretty much stuck on this step. I get 66 bits at the end of the script execution. It should actually be 64. And the value is incorrect too. I have tried reading algorithm in many sites and PDFs but no where is there a mention of truncating the bits. How is one supposed to get 64 bits if $H_0$ to $H_7$ values are more the 32 bits?

Answer 1

All the arithmetic in SHA-256 should be 32-bit, it can be implemented at a low level using only 32-bit registers. If you use a representation that can go over 32 bits, then you need to truncate back to 32 bits on every calculation in your chosen language where it will not do so itself - i.e. on every addition.