Tally Mark Arithmetic

+ concatenate!

-pair off the smaller subrahend from the bigger. Difference is what is left

* for each tally mark in the first factor, make a copy of the second. Then glue 'em.

//To get b//a, chop a out of b and keep track of the number of chops. (c). Then c = b//a

% This is the number of marks remaining after chopping

Drawback Not very compact.

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Denominational Numbering Systems

Roman Numeral Values

• M is 1000
• D is 500
• C is 100
• L is 50
• X is 10
• V is 5
• I is 1

Borrowing Thesea are the allowable borrowing combinations.

• CM is 900
• CD is 400
• XC is 90
• XL is 40
• IX is 9
• IV is 4

parse (v. i.) to derive meaning [from symbols]

Parsing We add up the values, using the borrowing conventions when we can.

Arithmetic is PITA.

Money!! How do you count out n dollars using as few bills as possible. Make this explanation as SIMPLE as possible but be complete.

Base Numbering Systems

These are denominational

1
2
4
8
16
.
.

If you are in base b: 1, b, b**2, b**3 ......

528 in base 2

1        0
2        0
4        0
8        0
16       1        0
32       0       16
64       0       16
128      0       16
256      0       16
512      1       16
1024     0      528

1000010000

528 in base 4

1       0
4       0
16      1       0
64      0      16
256     2      16
1024    0     528


20100(4) = 528


10 00 01 00 00
 2  0  1  0  0

base 8

1 000 010 000
1  0   2   0    →  0o1020

0o1020 = 528 = 0b1000010000

base16:  hexadecimal numbers

alphabet = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}

10 0001 0000
 2   1    0

 0x210

134324 % 10 = 4
134324 // 10 = 13432  (three blind mice)

x number
b base

x//b is the number with the last digit chopped.
x% b is the last digit.

321

321   1
160   0
 80   0
 40   0
 20   0
 10   0
  5   1
  2   0
  1   1
  0   0

  321 = 0b101000001

  LITTLEENDIAN