MGMT 1000 Lecture Notes - Lecture 10: Tsinghua Bamboo Slips, Multiplication Table, Binary Number
MGMT 1000 Lecture 10 Notes – Multiplication Table
Introduction
• The easiest way to create a multiplication table is to treat multiplication as multiple
additions.
• Each column (or row) represents the addition of the value in the row (or column) being
created.
• Thus, in the following table, you can see that 5×8 is equivalent to5×7+5=40.
• The familiar decimal multiplication table appears with the example just given indicated.
• The same technique can be applied to the base 8 multiplication table
• Note in the foregoing table that 3×3=3× 2+3.
• Note, though, that counting up 3 from 6 (or adding 3 to 6) results in a carry after 7 is
reached
• →→→.
• The base 2 multiplication table is almost trivial, since 0 times anything is 0 and 1 times 1
is itself
• 0 1 0 0 0 1 0 1.
• Because the binary multiplication table is so simple, it turns out that multiplication can
be implemented in a computer fairly easily.
• There are only two possible results
• If the multiplier is 0, the answer is 0, even if the multiplicand is a nonzero multi-digit
number.
• If the multiplier is 1, the multiplicand is brought down as the result.
• You might recognize the multiplication table as a Boolean AND function.
• If you recall that decimal multi-digit multiplication is performed by multiplying the
multiplicand by each digit of the multiplier, shifting the result of each multiplication to
line up with the multiplier, and adding up the results.
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