Decomposition into Powers of 2 Earlier "the decomposition of one number into its binary components" and "the powers of two" were mentioned as important in the multiplication process.
Three different representations of 92, 25, and 15 are shown. To multiply 10 by 3, find the 3rd multiple of To multiply 3 by 10, find the 10th multiple of 3. Written Work The Rhind Papyrus was not written in more ancient hieroglyphics but in Hieratic notation.
Multiplication by Decomposition To multiply two numbers using powers of 2: 1st:. Use two side-by-side columns of numbers. The left column will contain the multiplier and powers of two.
The right column will contain multiples of the multiplicand and the product. Additional columns of checks or marks and of identified "doubles" may be placed as desired by the scribe. Begin at the top of the left column and fill the column in order with the powers of two until you have reached the multiplier. If the multiplier is a power of two write this row twice. If the multiplier is not a power of two, write the multiplier only once at the bottom of the left column. Create the remaining entries in the right column by doubling the number in the row above it.
Stop when you have matched all the rows of the left column except for the multiplier. Check or mark the powers of two required to decompose the multiplier. In the example above the multiplier is The scribe may create a new column or use the existing right column. Division Yes, division may be completed by repeated subtraction.
The left column will contain powers of two and eventually the quotient. The right column will contain multiples of the divisor. Begin at the top of the left column and fill the column in order with the powers of two until you have reached the dividend. Stop when the "double" is as large as the dividend. Ask them what are the advantages and disadvantages compared to the method they usually use.
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Check out our best selling card games now available at amazon. For instance you would like to multiply by. Two columns are set up as shown below: you start with both factors in the first row. In the next row you double the value of and half the value of. If is odd the remainders are ignored. Simultaneously you can, however, mark the rows with odd , that is where the division by 2 has a remainder. This will be repeated until the number in halves column is reduced to.
Then the sum of marked numbers in the doubles column gives the product. The idea behind the scene is the conversion of one of the factors more precisely of the multiplier into binary form by repeated dividing by two and keeping track of the remainder. Actually reading the remainders from bottom to top we get the binary form of the halved factor. In our case , i. If is the smallest of both factors, then the number of rows is clearly given by the smallest satisfying the inequality , i.
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