# Assignment: Historical Counting Systems Problem Set

**Counting Board And Quipu**1) In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing. 2) Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part

**a**on the left and moving to the right for parts

**b**through

**d**.)

(a) 232

(b) 5065

(c) 23,451

(d) 3002

**Basic Base Conversions**1) 423 in base 5 to base 10 2) 3044 in base 5 to base 10 3) 387 in base 10 to base 5 4) 2546 in base 10 to base 5

**Mayan Conversions**

*Convert the following numbers to Mayan notation. Show your calculations used to get your answers.*1) 135 2) 234 3) 360 4) 1,215 5) 10,500 6) 1,100,000

*Convert the following Mayan numbers to decimal (base*

*-10) numbers. Show all calculations.*

7) | 8) |
9) |
10) |

*Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.*(To think about but not write up: Bidwell claims that only these entries are needed for “Mayan multiplication.” What does he mean?)

**Binary and Hexadecimal Conversions**

*Modern computers operate in a world of “on” and “off” electronic switches, so use a*

**binary**counting system – base 2, consisting of only two digits: 0 and 1.

*Convert the following binary numbers to decimal (base*

*-10) numbers.*1) 1001 2) 1101 3) 110010 4) 101110

*Convert the following base-10 numbers to binary*5) 7 6) 12 7) 36 8) 27

*Four binary digits together can represent any base-10 number from 0 to 15. To create a more human-readable representation of binary-coded numbers, hexadecimal numbers, base 16, are commonly used. Instead of using the 8,13,1216 notation used earlier, the letter A is used to represent the digit 10, B for 11, up to F for 15, so 8,13,1216 would be written as 8DC.*

*Convert the following hexadecimal numbers to decimal (base*

*-10) numbers.*

*9) C3 10) 4D 11) 3A6 12) BC2*

*Convert the following base-10 numbers to hexadecimal*

*13) 152 14) 176 15) 2034 16) 8263*