Numbers
Get the file numbers.pdf; this is the reading for this (short) part of the course.
Tally Mark Arithmetic To represent a number, we make a I for each unit. F'rinstance the decimal number 5 is represented by IIIII.
Let's do arithmetic with them!
680 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII + IIII + II = IIIIII (concatenate) - IIIIII - III IIIII - II IIII - I III * IIIIII * IIII IIIIIIIIIIIIIIIIIIIIIIII (for each of the tallies in the second make a copy of the first; glue copies) // (integer division) % (mod) 45//8 = 5 integer division 45%8 = 5 mod (short for modulus) IIIIIII//III I + IIII/III II + I//III II IIIIIII%II = I I III III
Roman Numerals
I 1 V 5 X 10 L 50 C 100 D 500 M 1000 Borrowing conventions IV 4 IX 9 XL 40 XC 90 CD 400 CM 900
MCMLVII → 1957 MMXXII → 2022 2991 → MMCMXCI
Arithmetic
11
289 CCLXXXIX
577 DLXXVII
--- ----------
866 DCCCLXVI
Ugh.
Arithmetic gets plug ugly
denominational numbering system
Confect a scheme to count out an integert number
of dollars with as few bills as possible.
1
2
5
10
20
50
100
481
1
2
4
8
16
32
64
128
256
512
1024
.
.
.
632
1024 0 632
512 1 120
256 0 120
128 0 120
64 1 56
32 1 24
16 1 8
8 1 0
4 0
2 0
1 0
0b1001111000 (binary)
632
1
7
49
343
2401
2401 0 632
343 1 289
49 5 44
7 6 2
1 2 0
1562
Denoninational Numbering Systems
Base Numbering Systems