READERS' FEEDBACK

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The Editors and Readers of COMPUTE!

Computer Counting
I don't understand the difference between ASCII, hexadecimal, and decimal numbers.

ASCII (pronounced "as-key") is an acronym for American Standard Code for Information Interchange. It is a standard code used for communication between computers. Among other things, it lets different types of computers communicate with each other using telephone modems.
    Each ASCII number stands for a character. For instance, the ASCII code 65 stands for the uppercase letter A. Because an ASCII number consists of one byte containing eight bits, there are 256 possible code numbers (2 to the eighth power). But only the first 128 characters are defined by ASCII, while the remaining 128 characters are different on each computer. Some computers tinker with the first 128 codes, too, creating their own version of ASCIIsuch as PETASCII (Commodore ASCII) or ATASCII (Atari ASCII). Departures from regular ASCII can cause compatibility problems when these computers try to communicate with other computers.
    The figure below shows the 128 standardized characters which make up the ASCII character set:

	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
0	0000000 NUL   0 0000001 SOH ^A 1 0000010 STX ^B 2 0000011 ETX ^C 3 0000100 EOT ^D 4 0000101 ENQ ^E 5 0000101 ACK ^F 6 0000111 BEL ^G 7 0001000 BS ^H 8 0001001 HT ^I 9 0001010 LF ^J 10 0001011 VT ^K 11 0001100 FP ^L 12 0001101 CR ^M 13 0001110 SO ^N 14 0001111 SI ^O 15 001000 DLE ^P 16 0010001 DC1 ^Q 17 0010010 DC2 ^R 18 0010011 DC3 ^S 19 0010100 DC$ ^T 20 0010101 NAK ^U 21 0010110 SYN ^V 22 0010111 ETB ^W 23 0011000 CAN ^X 24 0011001 EM ^Y 25 0011011 SUB ^Z 26 0011100 ESC   27 0011101 FS   28 0011101 GS   29 0011110 RS   30 0011111 US   31 0100000 SPACE 32 0100001 ! 32 0100010 " 34 0100011 # 35 0100100 $ 36 0100101 % 37 0100110 & 38 0100111 ' 39 0101000 ( 40 0101001 ) 41 0101010 * 42 0101011 + 43 0101100 , 44 0101101 - 45 0101110 . 46 0101111 / 47 0110000 0 48 0110001 1 49 0110010 2 50 0110011 3 51 0110100 4 52 0110101 5 53 0110110 6 54 0110111 7 55 0111000 8 56 0111001 9 57 0111010 : 58 0111011 ; 59 0111100 < 60 0111101 = 61 0111110 > 62 0111111 ? 64 1000000 @ 64 1000001 A 65 10000010 B 66 1000011 C 67 1000100 D 68 1000101 E 69 1000110 F 70 1000111 G 71 1001000 H 72 1001001 I 73 1001010 J 74 1001011 K 75 1001100 L 76 1001101 M 77 1001110 N 78 1001111 O 79 1010000 P 80 1010001 Q 81 1010010 R 82 1010011 S 83 1010100 T 84 1010101 U 85 1010110 V 86 1010111 W 87 1011000 X 88 1011001 Y 89 1011010 Z 90 1011011 [ 91 1011100 \ 92 1011101 ] 93 1011110 ^ 94 1011111 _ 95 1100000 ` 96 1100001 a 97 1100010 b 98 1100011 c 99 1100100 d 100 1100101 e 101 1100110 f 102 1100111 g 103 1101000 h 104 1101001 i 105 1101010 j 106 1101011 k 107 1101100 l 108 1101101 m 109 1101110 n 110 1101111 o 111 1110000 p 112 1110001 q 113 1110010 r 114 1110011 s 115 1110100 t 116 1110101 u 117 1110110 v 118 1110111 w 119 1111000 x 120 1111001 y 121 1111010 z 122 1111011 { 123 1111100 | 124 1111101 } 125 1111110 ~ 126 1111111 DEL 127
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    As you examine the figure, you'll notice some rather unusual designations. Not all ASCII numbers stand for characters you would normally recognize. These are control codes and are considered to be nonprinting machine instruction characters. In other words, instead of printing a character on the screen, they perform some function-such as clearing the screen, moving the cursor, or forcing a carriage return or linefeed.
    To answer the second part of your question, decimal and hexadecimal are just two different numbering systems, not coding systems like ASCII. Decimal is the system we normally use, sometimes called base 10 because it's based on 10 digits-0 through 9. Hexadecimal is base 16 and uses 16 digits-0 through 9 plus A, B, C D, E, and F (any symbols could have been chosen to represent the extra six digits, but A-F were selected because they're commonly available on keyboards).
    When counting in hexadecimal, just as in decimal, you don't start using two-digit numbers until you've run out of one-digit numbers. For example, in decimal you count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and then 10. In hexadecimal, you would count 0, 1, 2, 3, 4,5,6,7,8,9, A, B, C, D, E, F, and then 10. Notice that A in hexadecimal equals 10 in decimal, B equals 11, C equals 12, and so on. Therefore, hexadecimal 10 equals decimal 16. In any numbering system, the first two-digit number-represented as 10-always equals the base of that system. (Incidentally, we might be using the hexadecimal system for everyday counting if humans were born with 16 fingers instead of 10.)
    It's not too important to learn hexadecimal unless you want to write programs in machine language. Machine language programmers use the hexadecimal numbering system (and sometimes the base 8 system, called octal) because it's a more compact way of writing binary numbers and a more efficient way of visualizing binary patterns. Binary, in turn, is the base 2 numbering system-it uses only the digits 0 and 1. Computers "think" in binary and are programmed that way on the machine language level. But binary numbers take up lots of space when written down, and they are difficult to read. For instance, the binary number 11010010 is eight digits long and is hard to interpret at a glance. Expressed in decimal, 11010010 equals 210-a threedigit number that obscures the binary pattern. Expressed in hexadecimal, 11010010 equals D2, a more compact number which an experienced programmer can break down into two parts-D = 1101 and 2 = 0010. This can be very important in machine language programming.
    Because machine language programmers are likely to encounter decimal, hexadecimal, and binary numbers in books, magazines, and program listings, special symbols have been agreed upon to. keep the different systems from being confused with each other. Otherwise, the number 100 could be interpreted to have a decimal value of 100 in decimal, 64 in hexadecimal, or 4 in binary. Needless to say, this could result in a programming snafu that would leave the computer pretty confused, too. Many programmers use the dollar sign ($) to denote hexadecimal and the percent sign (%) to denote binary. So $FF means hexadecimal FF, which equals 255 in decimal. Other programmers use the letter H to represent hexadecimal, so $FF would be written FFH. A number with no special symbol is assumed to be decimal.
    For a more thorough discussion of these numbering systems, consult a programming book, such as Machine Language for Beginners, Programming the VIC, Programming the 64, or Programming the PET/CBM from COMPUTE! Books.