How to generate a list of first N binary numbers in Oracle SQL?

In my recent post I showed how to convert a decimal number (i.e. an integer) into a binary string. We can build upon that technique to answer the question:

WITH x AS (
SELECT LEVEL n
FROM dual
CONNECT BY LEVEL<=50
)
SELECT x.N, y.bin
FROM x, LATERAL (SELECT LISTAGG(SIGN(BITAND(x.N, POWER(2,LEVEL-1))),'') 
                        WITHIN GROUP(ORDER BY LEVEL DESC) bin
                 FROM dual
                 CONNECT BY POWER(2, LEVEL-1)<=x.N) y

Note the LATERAL keyword (Oracle 12c new feature) that enables us to reference “x” in the inline view “y”. In pre-12c world, we would have to use TABLE/CAST/MULTISET function composition to achieve the same result:

WITH x AS (
SELECT LEVEL n
FROM dual
CONNECT BY LEVEL<=50
)
SELECT x.N, y.column_value bin
FROM x, TABLE(CAST(MULTISET(
          SELECT LISTAGG(SIGN(BITAND(x.N, POWER(2,LEVEL-1))),'') 
                 WITHIN GROUP(ORDER BY LEVEL DESC) bin
          FROM dual
          CONNECT BY POWER(2, LEVEL-1)<=x.N) AS sys.odcivarchar2list)) y

The idea used in the following query is based on a totally different approach. It builds a string of “0”s and “1”s in a loop until its length reaches a desired value:

WITH x(v, n) AS (
SELECT column_value, 1
FROM TABLE(sys.odcivarchar2list('0','1'))
UNION ALL
SELECT x.v || t.column_value, x.n+1
FROM TABLE(sys.odcivarchar2list('0','1')) t JOIN x on LENGTH(x.v)=n
WHERE n<=CEIL(LOG(2,50))
), y AS (
SELECT NVL(LTRIM(x.v,'0'),'0') bin, ROWNUM-1 dec
FROM x
WHERE n=(SELECT MAX(n) FROM x)
)
SELECT *
FROM y
WHERE dec<=50

To better understand the above query, try the following one:

SELECT *                            
FROM TABLE(sys.odcivarchar2list('0','1')), 
     TABLE(sys.odcivarchar2list('0','1')),
     TABLE(sys.odcivarchar2list('0','1')),
     TABLE(sys.odcivarchar2list('0','1'))

If we put enough tables in the Cartesian product and concatenate all column_value columns in a single character string expression, we will achieve our goal. The challenge with this approach is to dynamically change the number of the tables in the FROM clause. This can be simulated in the recursive WITH clause by repeatedly adding more and more collections of bits (0 and 1).

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Integer to Binary Conversion in Oracle SQL

Interestingly enough, Oracle does not have a built-in function to convert Decimal numbers (i.e. integers) into Binary. This post offers an elegant way of doing so.

The following script is intended to be executed in SQL*Plus, so it uses some SQL*Plus commands:

column bin format a40
undefine N
SELECT LISTAGG(SIGN(BITAND(&&N, POWER(2,LEVEL-1))),'') 
       WITHIN GROUP(ORDER BY LEVEL DESC) bin
FROM dual
CONNECT BY POWER(2, LEVEL-1)<=&&N;

Result (for N=400):

BIN
-------------
110010000

Result (for N=1401):

BIN
------------
10101111001

Explanation:

How many digits may the resulting binary string have? The answer comes from Math: not more than LOG(2, N) + 1. Let’s first generate a numeric range from 1 to LOG(2,N)+1:

SELECT LEVEL
FROM dual
CONNECT BY LEVEL<=LOG(2,&N)+1

Result (for N=1401):

 LEVEL
------
     1
     2
     3
     4
     5
     6
     7
     8
     9
    10
    11

Alternatively, we can use mathematically equivalent condition in the CONNECT BY clause using POWER instead of LOG function:

SELECT LEVEL
FROM dual
CONNECT BY POWER(2,LEVEL)<=&N*2

or

SELECT LEVEL
FROM dual
CONNECT BY POWER(2,LEVEL-1)<=&N

Now, we will check every bit of the desired result (i.e. binary representation of N) by using BITAND function:

SELECT LEVEL, BITAND(&&N, POWER(2,LEVEL-1)) bit
FROM dual
CONNECT BY POWER(2,LEVEL-1)<=&&N

Result (for N=12):

LEVEL        BIT
----- ----------
    1          0
    2          0
    3          4
    4          8

Positive values in the bit column refer to a bit 1 in the corresponding position (in reverse order) of the binary value. It’s easy to turn those values to 1 by using SIGN function:

SELECT LEVEL, SIGN(BITAND(&&N, POWER(2,LEVEL-1))) bit
FROM dual
CONNECT BY POWER(2,LEVEL-1)<=&&N

Result (for N=12):

LEVEL        BIT
----- ----------
    1          0
    2          0
    3          1
    4          1

Here, we can see that we need to concatenate the values in the bit column in reverse order. This is very easy to do using LISTAGG function:

SELECT LISTAGG(SIGN(BITAND(&&N, POWER(2,LEVEL-1))),'') 
       WITHIN GROUP(ORDER BY LEVEL DESC) bin
FROM dual
CONNECT BY POWER(2,LEVEL-1)<=&&N

Result (for N=12):

BIN
----------
1100

Note that we sorted all the rows in descending order of the LEVEL to obtain the correct order of bits.

My Oracle Group on Facebook:

If you like this post, you may want to join my new Oracle group on Facebook: https://www.facebook.com/groups/sqlpatterns/

Would you like to read about many more tricks and puzzles?

For more tricks and cool techniques check my book “Oracle SQL Tricks and Workarounds” for instructions.