Next, we will consider how to make a program that adds 1 to any number between 0 and 9.

First we need a way to represent the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with only the bit values 0 and 1. The following table shows how we will do it.

Table 1

 number  representation
      0  0000
      1  0001
      2  0010
      3  0011
      4  0100
      5  0101
      6  0110
      7  0111
      8  1000
      9  1001

Next we need a table indicating what the answer is for each possible number 0 to 9.

Table 2

 number  answer
      0   1
      1   2
      2   3
      3   4
      4   5
      5   6
      6   7
      7   8
      8   9
      9  10

Next, we rewrite this table as:

Table 3

 number  answer
      0  01
      1  02
      2  03
      3  04
      4  05
      5  06
      6  07
      7  08
      8  09
      9  10

Next, we use table 1 to write table 3 with 1's and 0's. That is, we replace all 0's in table 3 with 0000, all 1's with 0001, and both 2's with 0010, etc. This gives us the following table.

Table 4

 number  answer
   0000  00000001
   0001  00000010
   0010  00000011
   0011  00000100
   0100  00000101
   0101  00000110
   0110  00000111
   0111  00001000
   1000  00001001
   1001  00010000

Next, we write table 4 as data in memory.

Table 5

 label       address             data         comment
                 (number)          (answer)
add1tabl 0000000001000000  0000000000000001
         0000000001000001  0000000000000010
         0000000001000010  0000000000000011
         0000000001000011  0000000000000100
         0000000001000100  0000000000000101
         0000000001000101  0000000000000110
         0000000001000110  0000000000000111
         0000000001000111  0000000000001000
         0000000001001000  0000000000001001
         0000000001001001  0000000000010000

This kind of table is called a lookup table because you can look up the answer in it. A lookup table can be made to do any function with a limited number of possible inputs. This function is called 'increment' (add 1) and has 10 possible inputs: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Next, we decide where the number to increment and the answer will be stored in memory.

 label       address             data                  comment

         0000000000000000  0000000000100000       start0000000000001000
         0000000000000001  0000000000001001        number to increment
         0000000000000010  0000000000000000        answer

Next, we write the program. The program is a list of instructions that tell the processor how to manipulate data. That is, the program tells the processor from where and to where copy data.

 label       address             data                  comment

instr_1  0000000000001000  0000000000000001        from address 
         0000000000001001  0000000000001100        to address
         0000000000001010  0000000000001111        'to' bits to copy to
         0000000000001011  0000000000110000        instr.addr.and rot.
instr_2  0000000000001100  0000000001000000        from address 
         0000000000001101  0000000000000010        to address
         0000000000001110  0000000011111111        'to' bits to copy to
         0000000000001111  0000000001000000        instr.addr.and rot.
instr_3  0000000000010000  0000000000000000        from address 
         0000000000010001  0000000000000000        to address
         0000000000010010  0000000000000000        'to' bits to copy to
         0000000000010011  0000000001000000        instr.addr.and rot.

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