Tally Mark Arithmetic
+ concatenate!
- You can only subract a smaller number from a bigger number. Pair off the elements and delete the pairs. What's left is the difference.
* for each tally in the first, make a copy of the second. glue 'em.
//for b//a chop a out b. Keep count of the number of chops.
%How many are left over afer the chopping.
Downside It's not compact.
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Large numbers are burdensome.
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 horrible!
Money!! How do you count out n dollars using as few bills as possible. Make this explanation as SIMPLE as possible but be complete.
Start with biggest and count out as many as you can. repeat for lower denominations.
Greed is good!
Base Numbering Systems
These are denominations
442denom qty left 1 2 4 8 16 32 64 128 256 512 0 442
denom qty left 1 0 0 2 1 0 4 0 2 8 1 2 16 1 10 32 1 26 64 0 58 128 1 58 256 1 186 512 0 442
read up: 442 = 0b110111010
Do this in base 4.
442 = 12322412322 1 10 11 10 10 Base 8 "octal numbers" convert 442 into octal. 110 111 010 6 7 2 → 0o672 base 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F} 442 in hexadecimal 1 1011 1010 1 B A → 0x1BA923840324908890432903824980423 % 10 = 3 923840324908890432903824980423 // 10 = 92384032490889043290382498042 three blind mice principle x number b base x//b is the number with the last base b digit amputated x%b is the last base-b digit. base 5 444 4 88 3 17 2 3 3 0 0 3234 littleendian method.