Ethiopian Binary Math
  The Ethiopians invented a process of halfing and doubling the factors of multiplication to find the correct quantity when trading goods. The Web Program below shows a way Ethiopian Binary Math may have been used by traders to configure a market stall to total orders for goods with very little counting or using times tables.
ETHIOPIAN MARKET STALL PROGRAM
Click to See Demonstration Videos Below
The following steps demonstrate how to use the Binary Market Stall to give a customer (X) units of a (Y) number of potatoes. For example (5 X 6). The customer might say 'Double my Y quantity by this X quantity.'
Step 1:  Double click stone in the upper left corner of top brown box. New stones will appear stacked in center of brown box and the counter will show (factor) number of stacked stones (X=5).
Step 2: Left click on stacked stones and drag to position, one on the left and one on the right, in the bottom box until all stacked stones are in the bottom box.
Step 3: Double click right most mini-potatoes in blue box positioned above white stalls. New potatoes will appear stacked in white stall below clicked potato and the counter will show (factor) unit number of stacked potatoes (Y=6).
Step 4: Left click on stacked potatoes and drag to position in the bottom of the stall.
Step 5A: Double click or drag the stones on the right, not including an extra stone, in the bottom box to put these back in the top box.
Step 5B: If there is an extra or remainder stone drag it to the brown box under the leftmost white stall with potatoes.
Step 5C: If there is no extra or remainder stone leave brown box under leftmost white stall with potatoes empty.
Step 6: Double click leftmost white stall with potatoes to send potatoes to next stall. The number of potatoes will double but appear stacked. Briefly place mouse on a potato then remove and you can use arrow keys to separate stacked potatoes or else click a potato to drag and reposition separate from its partner. The number of potatoes will appear above the stall. Click the red button to show a rectangle. When the rectangle shows, and you left click in a stall, potatoes will move up or down toward the mouse position.
Step 7: Reposition stones in bottom box to get the same number on left and right again. If there is 1 stone remaining drag it to the leftmost stall with potatoes and the distribution of potatoes is done. If there are more than 1 stone remaining. repeat steps 5 through 6.
The product will be the sum of potatoes in the stalls. (24 + 6 =30 = 5 X 6).
* You may half and distribute all stones before you distribute potatoes. See Video Below.
 To Reset, Double Click a Pyramid Stack of Potatoes.
 
Videos
 
 

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  • Click CLEAR ANSWERS. Then enter factors between 2 and 25 in each textbox.
  • Click green boxes on the left to see the answer for the number in the box above divided by 2. The answer's remainder of 0 or 1 will display to the right of the number divided above.
  • The remainders to the right of the textbox and the green boxes are the binary numerals or factors of the binary or doubling place values.
  • The next column to the right of the remainders are the binary or doubling place values.
  • See horizontal display of 0 and 1 numerals at the bottom with place values above these numerals.
  • The next column gives the unit quantities of the goods traded. Such as a dozen or more or less
  • The total quantity of a row will equal the binary numeral 0 or 1 times the doubling factor or place value times the unit quantity.
  • The total quantities of each row are then added together. Explore More on Bases

 

 
Binary Math and Computers
So, the 1's and 0's of binary math were configured by early Ethiopian traders to select doublings of quantities to distribute proper amounts of goods. Today the 1's and 0's of binary math represent in computers data such as text, images and sound. The market stall is very much like a computer organizing inputs of 1's and 0's to output solutions necessary for managing our daily life. Use the simulator below to explore the logic of computer circuits below. Click Full screen mode after reading instructions on the webpage below.
   
 

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