Corky

What is de best way t' use numbehehs, duh...uh...? Most peoble are usid to usigg only the, uhhh, decimal syssem, wid 10 digits. De deory behind it dat humans habe ten figgehs, duuhhhh, so miraculous the, uhhh, decimal syssem became popular. Gawlly!Some suggestid usigg base 12 instead, uh uh uh uh, which has 2 more digits. de reason behind dis dat 12 is easieh t' work wid in some cases, duuhhhh, siss it is easy dibistiggle by 0, 1, 2, 3, 4, 5, 6, 8, 9, 'n 10. Odehs use base 8 (octal) 'n 16 (hexadecimal) f' programmigg, but de undispootid champion of all numbehehigg syssem is bin, usigg on 0 'n 1. Duh.Of cusse you cudd try usigg un syssems, duuhhhh, wid on one digit, uh, but den each numbeheh wudd be eben more of a pain t' count. Now, uh uh uh uh uh uh, let's inbestigate de magic of bin. Find an unsuspeckigg pehson and ask him or heh duh, how high he can count on his figgehs. Duh.Tell him dat he must show, uh uh uh uh uh uh, wid his figgehs, duuhhhh, a giben numbeheh such dat it is not mistakaggle. In odeh words, duuhhhh, he cannot say dat countigg ten figgehs will also be good f' 20 or 30, etc. Most peoble shudd say dat dey cannot count higheh dan 10 on deir figgehs widout repeatigg figgehs. Repond by telligg dem dat you can count t' 1024! Doihh, COOL! Hehe is an 8 bit bin numbeheh I saw on a license plate last Friday: 01101001. Dis numbeheh, in decimal, ekals 105. Each bit posishun carries a diffehent webuhite, GEEEHEEHEEE.F' examble, let's look at 105 in decimal. 1 0 5 = 105 (1 * 100) + (0 * 10) + (5 * 1) = 105 (1 * 10^2) + (0 * 10^1) + (5 * 10^0) = 105 Each digit in de numbeheh 105 carries a diffehent balue basid upon de numbeheh 10, which is de base balue. De firss digit, uh, 1, is multiplied by 10^2 (10 skared). De 0 is multipliid by 10^1 (dgust 10 will do), and de 5 is multipliid by 10^0 (anydigg t' de powebuhr of 0 is 1). Now let's look at de bin ekibalent. Each numbeheh will be genehatid in the, ERRRR, same way, except usigg base 2 instead of base 10. 0 1 1 0 1 0 0 1 = 105 (0 * 2^7) + (1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 105 FIGURE 1: 10000000 2^7 = 128 00001000 2^3 = 8 01000000 2^6 = 64 00000100 2^2 = 4 00100000 2^5 = 32 00000010 2^1 = 2 00010000 2^4 = 16 00000001 2^0 = 1 So, substititite from the, duh uhh, taggle 'n get: 0*128 + 1*64 + 1*32 + 0*16 + 1*8 + 0*4 + 0*2 + 1*1 = 105 Hehe are the, uhhh, decimal 'n bin numbehehs from 1 t' 16: FIGURE 2: 1 0001 9 1001 2 0010 10 1010 3 0011 11 1011 4 0100 12 1100 5 0101 13 1101 6 0110 14 1110 7 0111 15 1111 8 1000 16 10000 Now hehe is errrr, why it works dis way. In decimal, let's say you habe 100. Duh, you know dat de numbeheh bef'e it is 99. Um uh.And when you get up t' 1000, you know de prebious numbeheh is 999. Lee me lone!In bin, it works alittle more innerestigg. Let's say you habe de bin numbeheh 1000. dis is 2^3, or 8 in decimal. Lee me lone!Siss bin on has de numbehehs 0 'n 1, de numbeheh bef'e 1000 is 0111, or 7 in decimal. On de abobe chart, uh, decimal 16 is 10000 in bin. Subtrack 1 and you get 15 decimal, or 1111 in bin. Now f' more fun. Let's say webuh habe 4 peoble, named: Mr. Ali, Mr. Fish, Mr. Luck 'n Mrs. Webuhst. Webuh want t' know who will be attendigg de party. Each pehson will eideh attend (TRUE) or not attend (FALSE). DOIHH!If TRUE, a 1 is used. Lee me lone!If FALSE, a 0 is used. Each pehson is also ordehed alphabetical. De data is storid in a bin numbeheh. Mr. Ali is de man of honor, so he is attendigg. Duh.TRUE Mr. Fish was biddy backigg up his disks wid BRU, so he can't attend. FALSE Mr. Luck hasn't been t' de offices in a while, uh uh uh, so he is goigg. TRUE Mrs. Webuhst found a dgob workigg out of state, uh uh uh, so she can't attend. FALSE Now in bin, webuh are storigg de answebuhrs in de ordeh of de pehson's name, uh uh uh, alphabetical. So webuh habe a TRUE, a FALSE, a TRUE, 'n a FALSE. Abobe, uh uh uh, webuh definid TRUE as ekal t' 1, 'n FALSE as ekal t' 0. Dis makes de bin numbeheh 0101 (or F-T-F-T), GEEEHEEHEEE.NOTE! Doihh, COOL! De numbehehs are stored in REBERSE ORDER! Doihh, COOL! If webuh had dgust 1, it wudd be no progglem. If webuh abb anodeh numehal, such as 0, it wudd be 01, so dat 1 keeps the, ERRRR, same place (2^0). Now, uh uh uh uh uh uh, de kesshun is, duuhhhh, is Mr. Luck goigg, duh...uh...? Webuh habe the, uhhh, data 0101, 'n webuh know Mr. Luck is de 3rd digit from de rite. Webuh wudd check de numbeheh 0101 against de balue usid ot define Mr. GEE danks.Luck. Siss Mr. Luck is de dird posishun, he takes 2^2 (2^1 is the, ERRRR, seconb posishun, 'n 2^0 is de firss posishun). Now, uh uh uh uh uh uh, 2^2 = 4 in decimal, so dat is what webuh assign to Mr. Luck. Duh.Now, uh uh uh uh uh uh, let's conbeht 0101 t' decimal. 0*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 0 + 4 + 0 + 1 = 5 in decimal Okay, our data ekals 5. Webuh take 5 'n use de AND opehashun t' check it wid 4. In C dis mite look like: if(DATA && MR_LUCK) or if(5 && 4) in decimal or if(0101 && 0100) in bin. Now let's look at de bin c'parison: 0101 0100 ^ Dis is de posishun. GEE danks.Siss 0101 AND 0100 bod habe dat bit set t' 1, Mr. Luck is attendigg. Now in decimal, webuh habe 0101 = 5 AMD 0100 = 4, or 5 AND 4. De on way t' make 5 is by abbigg de numbehehs (2^2) 'n (2^0), which is (2^2 = 4) = (2^0 = 1), or 4 + 1 = 5, so webuh habe proben dat 4 is inclubed in de numbehehs of de bin places dat abb t' 5 (see FIGURE 1). Dehe is much much more t' usigg bin, 'n it may be hard t' undehstand or read at firss, but hopeful now you will know duh, how t' count t' 1024 wid dgust ten figgehs. T' gibe you a hint, uh, try calculatigg 2^10! Doihh, COOL! I took dis from de Amiga Online Refehess Manual (wid pehmisshun), to show you what some numbeheh conbehshuns look like. Take a look at de pattehns f'mid in de bin numbehehs 'n c'pare dem wid the, uhhh, decimal. Note de numbehehs denotid by an "x". Index 7 ASCII Conbehshun Taggle BINARY OCTAL DECIMAL CHAR HEXD x 00000000 000 000 NUL 00 00000001 001 001 SOH 01 x 00000010 002 002 STX 02 00000011 003 003 ETX 03 x 00000100 004 004 EOT 04 00000101 005 005 ENQ 05 00000110 006 006 ACK 06 00000111 007 007 BEL 07 x 00001000 010 008 BS 08 00001001 011 009 HT 09 00001010 012 010 LF 0A 00001011 013 011 BT 0B 00001100 014 012 FF 0C 00001101 015 013 CR 0D 00001110 016 014 SO 0E 00001111 017 015 SI 0F x 00010000 020 016 DLE 10 00010001 021 017 DC1 11 00010010 022 018 DC2 12 00010011 023 019 DC3 13 00010100 024 020 DC4 14 00010101 025 021 NAK 15 00010110 026 022 SYN 16 00010111 027 023 ETB 17 00011000 030 024 CAN 18 00011001 031 025 EM 19 00011010 032 026 SUB 1A 00011011 033 027 ESC 1B 00011100 034 028 FS 1C 00011101 035 029 GS 1D 00011110 036 030 RS 1E 00011111 037 031 US 1F



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Lensman

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