# Print a table of numbers in decimal and 2**i bases

Computers live by binary. All programmers know binary.

But the 2**x bases are often neglected as non-practical, while they have beautiful relations to binary.

To show you one example of such a beatiful relation, 19 will be my testimonial.

19 10011 103 23 13 j

• 19 is decimal, included for clarity.

• 10011 is 19 in binary.

• 103, in base 4 is made starting from binary this way:

• log2(4) == 2, let us remember two.
• Pad 10011 so that it has a multiple of 2 length -> 010011
• Take digits 2 by 2 from left to right and treat them as 2-digits binary numbers:

• 01 -> 1
• 00 -> 0
• 11 -> 3

Done, 10011 in base-4 is 103.

For base 8, do the same but 3-by-3 as log2(8) = 3.

• 010 -> 2
• 011 -> 3

23, Done.

For base 16, do the same but 4-by-4 as log2(16) = 4.

• 0001 -> 1
• 0011 -> 3

13, Done.

Given a max number as input, you shall output a table

base-ten-i base-two-i base-four-i base-eight-i base-sixteen-i base-thirtytwo-i


for i that goes from 0 to n inclusive. Binary numbers are the epitome of the absolute minimum needed to work, so your code should be as short as possible.

Restrictions and bonuses

• Base-ten -> binary and binary -> Base-ten built-ins are considered loopholes as Base-a -> Base-b are.

• If you generate all the 2**i (for i > 2) bases by using the relations over mentioned you get a *0.6 bonus, but general base conversions (written by yourself) are allowed.

Example table

> 32
0 0 0 0 0 0
1 1 1 1 1 1
2 10 2 2 2 2
3 11 3 3 3 3
4 100 10 4 4 4
5 101 11 5 5 5
6 110 12 6 6 6
7 111 13 7 7 7
8 1000 20 10 8 8
9 1001 21 11 9 9
10 1010 22 12 a a
11 1011 23 13 b b
12 1100 30 14 c c
13 1101 31 15 d d
14 1110 32 16 e e
15 1111 33 17 f f
16 10000 100 20 10 g
17 10001 101 21 11 h
18 10010 102 22 12 i
19 10011 103 23 13 j
20 10100 110 24 14 k
21 10101 111 25 15 l
22 10110 112 26 16 m
23 10111 113 27 17 n
24 11000 120 30 18 o
25 11001 121 31 19 p
26 11010 122 32 1a q
27 11011 123 33 1b r
28 11100 130 34 1c s
29 11101 131 35 1d t
30 11110 132 36 1e u
31 11111 133 37 1f v
32 100000 200 40 20 10

• Downvoted because of "You must generate all the 2**i (for i > 2) bases by using the relations over mentioned". Requiring a specific algorithm removes a lot of what makes code golf interesting. You can ban built-in base conversion functions while still allowing a choice of algorithm. – xnor Sep 19 '15 at 1:02
• @xnor now using my method only gives a bonus, to give more freedom to golfers – Caridorc Sep 19 '15 at 9:21
• I'm not a fan of the bonus either. It effectively means you have to use either a built-in or your algorithm, and no other algorithm can be viable. – xnor Sep 19 '15 at 9:29
• @xnor built-ins are not allowed. A general converter will be shorter, so I give a bonus if you use my contrived conversion rules – Caridorc Sep 19 '15 at 9:32

# CJam, 54 * 0.6 = 32.4 bytes

q~){_5,f{)L@{2md@+\}h(%/Wf%W%{{\2*+}*_9>{'W+}&}%S\}N}/


Test it here.

For reference, here is a shorter solution which doesn't qualify for the bonus (at 39 bytes):

q~){:X5{SLX{2I)#md_9>{'W+}&@+\}h;}fIN}/

• I updated the challange, you may claim a 0.6* bonus if you used my method – Caridorc Sep 19 '15 at 9:37

# Pyth, 52 * 0.6 = 31.2 bytes

L?b+%b2y/b2YVUhQjd+NmjkX|_uL++GGHZ_McyNd]ZUQ+jkUTGS5


Test it online

My non-bonus answer is 39 bytes

M?G+g/GHH@+jkUTG%GHkVUhQjd+N|R0gLN^L2S5


# PHP, 232230233 217 * 0.6 = 130.2

no chance beating the golfing languages, but I liked the challenge.

for(;$d<=$n;$d++){echo' ',$d|0;for($k=$d,$b='';$k;$k>>=1)$b=($k&1).$b;for($w=1;$w<6;$w++,print"$z"|' 0')for($z='',$k=strlen($b);-$w<$k-=$w;$z=($e>9?chr($e+87):$e).$z)for($e=0,$y=1,$j=$w;$j--;$y*=2)$e+=$y*$b[$j+$k];}

• usage: prepend $n=32; or replace $n with 32 (or any other non-negative integer); call via cli
• If that is not accepted, replace $n with $_GET[n] (+6/+3.6) and call either in the browser
or on cli with php-cgi -f bases.php -n=32
• Replace the line break with <br> or prepend <pre> to test in browser
• may throw notices for undefined variables and unintialized string offsets in newer PHP versions.
Remove E_NOTICE from error_reporting (prepend error_reporting(0);) to suppress them.
• tested in 5.6

break down:

for(;$d<=$n;$d++) // loop decimal$d from 0 to $n { echo' ',$d|0; // print line break and decimal
for($k=$d,$b='';$k;$k>>=1)$b=($k&1).$b; // convert $d to binary for($w=1;$w<6;$w++,
print" $z"|' 0' // print number generated in inner loop (echo doesn´t work here) ) for($z='',$k=strlen($b);-$w<$k-=$w; // loop from end by$w
$z=($e>9?chr($e+87):$e).$z // prepend digit created in body ) for($e=0,$y=1,$j=$w;$j--;$y*=2)$e+=$y*$b[$j+$k]; // convert chunk to 2**$w }  major edit: • used some index magic to revamp the inner loop -> now works backwards on the whole string (no more padding, no more splitting or copying the binary) • moved parts of the loop bodies to the heads to eliminate braces • had to add 7 4 bytes to fix the decimal 0 results after the revamp # non-bonus version, 142 bytes for(;$d<=$n;$d++,print'
',$d|0)for($w=1;$w<6;$w++,print" $z"|' 0')for($k=$d,$y=1,$z='';$k&&$y<<=$w;$k>>=$w)$z=(9<($e=$k%$y)?chr($e+87):$e).$z;  PHP beats Python? Even if I added the 6 (3.6) bytes to make the snippet a program, I´d still beat Python (223*0.6=133.8 or 148 non-bonus vs. 158). Amazing. • I get an error 'Undefined variable: n :1' and I think that you can save 1 byte by removing a space after the for keyword in the outermost for-loop. – Yytsi Jul 3 '16 at 22:04 • @TuukkaX: see usage:$n must be define before the snippet. I found that byte, but thanks. And one more: "\n" -> physical line break. – Titus Jul 4 '16 at 15:33
• but I had to add 3 bytes to print the first 0. (that or 5 bytes to init the variable). – Titus Jul 4 '16 at 16:52

## Ruby, 80 bytes (non-bonus version)

m=ARGV[0].to_i;(0..m).each{|n|puts [10,2,4,8,16,32].map{|b|n.to_s(b)}.join(' ')}


## Python3 - 189, 167, 166 150 bytes

for i in range(int(input())+1):f=lambda b,n=i,c="0123456789abcdefghijklmnopqrstuv":n<b and c[n]or f(b,n//b)+c[n%b];print(i,f(2),f(4),f(8),f(16),f(32))


Saved 16 bytes with the help of @LeakyNun!

## Bonus version - 296 * 0.6 = 177.6 279 * 0.6 = 167.4 bytes

p=lambda b,c:"".join(str(int(b[i:i+c],2))for i in range(0,len(b),c))
z=lambda s:len(s)%2 and s or "0"+s
for i in range(int(input())+1):f=lambda n,b,c="0123456789abcdefghijklmnopqrstuv":n<b and c[n]or f(n//b,b)+c[n%b];v=f(i,2);d=z(v);print(i,v,p(d,2),p(d,3),p(d,4),p(d,5),f(i,32))


Slightly more readable version of the bonus version.

p=lambda b,c:"".join(str(int(b[i:i+c],2))for i in range(0,len(b),c))
z=lambda s:len(s)%2 and s or "0"+s
for i in range(int(input())+1):
f=lambda n,b,c="0123456789abcdefghijklmnopqrstuv":n<b and c[n] or f(n//b,b) + c[n%b]
v=f(i,2)
d=z(v)
print(i,v,p(d,2),p(d,3),p(d,4),p(d,5),f(i,32))

• I am pretty certain that the bonus does not apply. You are not using binary to produce the base 2**x numbers. – Titus Jul 4 '16 at 16:23
• @Titus Oh, I understood the bonus wrong then. I'll edit the byte count. Thanks! – Yytsi Jul 4 '16 at 16:24
• Pretty sure "0123456789abcdefghijklmnopqrstuv" is shorter than from string import* digits+ascii_lowercase – Leaky Nun Jul 4 '16 at 17:52
• @LeakyNun Oops. You're right. I only thought of how short it is to write digits+ascii_lowercase :D. Thanks! – Yytsi Jul 4 '16 at 17:53
• 150 bytes: for i in range(int(input())+1):f=lambda n=i,b,c="0123456789abcdefghijklmnopqrstuv":n<b and c[n]or f(n//b,b)+c[n%b];print(i,f(2),f(4),f(8),f(16),f(32)) (one line) – Leaky Nun Jul 4 '16 at 18:04