# Generate a Universal-binary-function Lookup Table

This is tangentially related to my quest to invent an esoteric programming language.

A table of the binary numbers 0 .. 15 can be used to implement a Universal Binary Function using indexing operations. Given two 1-bit inputs X and Y, all 16 possible functions can be encoded in a 4-bit opcode.

X Y  F|0 1 2 3 4 5 6 7 8 9 A B C D E F
- -    - - - - - - - - - - - - - - - -
0 0    0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
0 1    0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 0    0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
1 1    0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
-     -   - -   -   -   -   - -
0    ~X  ~Y ^   &   Y   X   | 1
ZERO    NOT-Y   AND         OR
NOT-X   XOR              ONE


So this set of 16 functions can be applied to binary inputs as the function

U(f,x,y): (f >> ((x<<1) | y)) & 1,

or

U(f,x,y): (f / 2^(x×2 + y)) % 2,

or with indexing or matrix partitioning.

It will be useful to know the most compact way to represent or generate such a table of values for any possible languages to be built upon this type of binary operation.

## The goal:

Generate this exact text output:

0101010101010101
0011001100110011
0000111100001111
0000000011111111


That's it! Shortest-code wins.

• I had an intuition that the APL-family would do well here. :) – luser droog Jul 25 '13 at 9:09
• Also related: A simple logic gate calculator – FireFly Nov 7 '14 at 13:39
• Are leading or trailing newlines accepted? – Titus Sep 20 '16 at 17:10
• Yes, extra newlines are fine. – luser droog Sep 20 '16 at 17:32

C 70 bytes

c,k=1,i;x(){putchar(48+i);i^=!(++c%k);c%16||(k*=2)+puts("");k>8||x();}


use recursive function... in https://ideone.com/ it compile and result:

0101010101010101
0011001100110011
0000111100001111
0000000011111111


even if in the compiler i use it does not compile...

• all functions that use global variables, if they use their value 0, can be ok only one time or only if global variable are at start 0 – RosLuP Sep 20 '16 at 21:00

for(;$i<64;$i++)echo($i%16?"":"\n").($i&2**($i>>4)?1:0);  86 Bytes for($i=1;$i<9;$i*=2)echo str_repeat(str_pad(decbin(2**$i-1),2*$i,0,0),16/(2*$i))."\n";  # PHP, 767068676157 45 bytes Now it´s worth it: code shorter than its output. :) for(;$x<64;$x++)echo$x%16?"":"
",$x>>$x/16&1;


run with -r.

runs through rows and columns in one loop:
$x/16 rounded is the row number, $x%16 the column and decimal value of the binary value we want to display:

In columns 0,16,32,48 ($x%%16 falsy) print a linebreak. If bit $x/16 is set ($x>>$x/16&1), print 1, else 0.

for(;$x<64;$x++)echo$x>>$x/16&1,\$x+1&15?"":"