## Case Study CS00012: Number representations in different bases

The problem: Sometimes in troubleshooting output it helps to see data in various encodings (i.e. hex, octal, binary, etc.).

The solution: This case study illustrates how Glee's base and representation serve this need almost directly.

1. Capture a string of text to be displayed in various forms
2. Convert to hex and capture in h
3. Convert to octal and capture in o
4. Convert to binary and capture in b
5. Columnize the various results int a table
6. Display the table.

Note: You can cut and paste these code fragments into the code pane of the Glee interpreter and experiment as you go along to see the actual operations live.

The Glee code:

'Now is the time'=>t;
'0'..'9','A'..'F'[t #asc %<16 #ea'+1>']=>h; \$\$ Hex
t#asc %<8 #ea'->3 %* ~'=>o;                 \$\$ Octal
t#asc %<2 #ea'->8 %* ~'=>b;                 \$\$ Binary
t ,| h  ,| o ,| b => output;                \$\$ Build Output table
output ,,(' : '(32 58 13 10 #asc))%* ,' :' \$;  \$\$ Display

The Output:
N : 4E : 116 : 01001110 :
o : 6F : 157 : 01101111 :
w : 77 : 167 : 01110111 :
: 20 : 040 : 00100000 :
i : 69 : 151 : 01101001 :
s : 73 : 163 : 01110011 :
: 20 : 040 : 00100000 :
t : 74 : 164 : 01110100 :
h : 68 : 150 : 01101000 :
e : 65 : 145 : 01100101 :
: 20 : 040 : 00100000 :
t : 74 : 164 : 01110100 :
i : 69 : 151 : 01101001 :
m : 6D : 155 : 01101101 :
e : 65 : 145 : 01100101 :

The play-by-play:

1. 'Now is the time'=>t; Collect the text under study in t.
2. '0'..'9','A'..'F'[t #asc %<16 #ea'+1>']=>h; \$\$ Hex. Convert to hex by creating an index and indexing from the hex characters. '0'..'9','A'..'F' creates the string of the 16 valid hex characters in the proper order...'F'[t #asc %<16 #ea'+1>'] indexes the characters out of the string. t #asc converts characters to their numeric ASCII index. %<16 represents the index in base 16. #ea'+1>' takes the elements of rep which are in origin 0 and adds 1 to make them origin 1 which Glee uses for indexing. This two digit result is enclosed to be used as a single unit. The resulting sequence of two number sequences is used to directly index out the hex representation.
3. t#asc %< 8 #ea'->3%* ~'=>o; \$\$ Octal. The octal conversion works the same as the hex conversion except no translation is needed for the output characters. The result is already in the valid set of digits 0 thru 7. However, depending on the size of the number in, we get from 1 to 3 digits out. We want to pad with leading 0's. #ea'->3%* ~' for each sequence element, pulls on leading 0's; converts to a string; and removes blanks. At each of these we convert to character form.
4. t #asc %<2 #ea' ->8%* ~'=>b; \$\$ Binary. For binary, we operate in the same fashion as with octal. However, we expect 8 binary digits per character where we only expected 3 for octal so we do an 8-right-take instead of a 3-right take.
5. t ,| h  ,| o ,| b => output; \$\$ Build Output table  . We build the output table by successively column catenating t ,| h ... the individual results. This really just creates sequences within sequences.
6. output ,,(' : '(32 58 13 10 #asc))%* ,' :' \$;  \$\$ Display. Here we use the dyadic sequence separation operator ,, using a two element right argument (' : '(32 58 13 10 #asc)). The first element goes between elements of the inner-most sequence. In this case it is just the colon character. On the outer sequence we want a space, a colon, and a line feed. This is most easily formed by taking the numeric ASCII codes (32, 58, and 10) and converting them to their character form. This three element string is inserted between the elements of the outer sequence and causes each character and its conversions to be displayed on a separate line.%* ,' :' \$;  \$\$ Display At this point we still have a sequence of sequences so we convert it to a simple character string %* and catenate on the final colon and display,' :' \$;

This completes the example. To better understand these operators and other things you can do with them, consult the operator pages according to the type of data you see being operated on.