Codes And Ciphers

#11 Base-8 Number System

#Cryptography

LECTURE #11: BASE-8 NUMBER SYSTEM

[INTRODUCTION]
Octal Numeral System or Oct for short, is a Base-8 Number System which uses the digits 0-7.

[HISTORY]
• By Native Americans
The Yuki language in California and the Pamean language in Mexico have octal systems because the natives count using the spaces between their fingers rather than the fingers themselves.

• By Europeans
In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number system based on 64 instead of 10. However, Swedenborg argued that for people with less intelligence than the king such a big base would be too difficult and instead he proposed 8 as the base. In 1718 Swedenborg wrote (but did not publish) a manuscript: "En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10" ("A new arithmetic (or art of counting) which changes at the Number 8 instead of the usual at the Number 10"). The numbers 1-7 are there denoted by the consonants l, s, n, m, t, f, u (v) and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule.

• In Fiction
Octal numeral system was also used in some of the TV series and movies like the film Avatar, wherein the Na'vi race employs an oct system, probably due to the fact that they have four fingers on each hand.

• In Computers
Octal became widely used in computing when systems such as PDP-8, ICL 900, and IBM mainframes employed 12-bit, 24-bit or 36-bit words. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits).

• In Aviation
Transponders in aircraft transmit a code, expressed as a four-octal-digit number, when interrogated by ground radar. This code is used to distinguish different aircraft on the radar screen.

[ENCRYPTION/DECRYPTION]

0 = A
1 = B
2 = C
3 = D
4 = E
5 = F
6 = G
7 = H
10 = I
11 = J
12 = K
13 = L
14 = M
15 = N
16 = O
17 = P
20 = Q
21 = R
22 = S
23 = T
24 = U
25 = V
26 = W
27 = X
30 = Y
31 = Z

[GAME]
Now, let's try what you learnt. Try to decrypt.

(1) 13 - 16 - 30 - 0 - 13 - 23 - 30
(2) 14 - 0 - 12 - 4 - 22
(3) 30 - 16 - 24
(4) 5 - 0 - 14 - 10 - 13 - 30

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