MGMT 1000 Lecture 9: MGMT 1000 Lecture 9 Notes
MGMT 1000 Lecture 9 Notes – Base 10
Introduction
• Since 3+6=9, the next column will have to carry to the next place, or 10, just as occurred
when we demonstrated counting in base 10, earlier.
• This knowledge should make it easy for you to create a base 8 addition tables.
• Try to create your own table before looking at the one
• Of special interest is the base 2 addition table
• + 0 1 0 0 1 1 1 10
• Clearly, addition in base 2 is going to be easy!
• Addition in base 2 (or any other base, for that matter) then follows the usual methods of
addition that you are familiar with, including the handling of carries that you already
know.
• The only difference is the particular addition table being used.
• There are practice problems representing multi-digit binary arithmetic and column
arithmetic at the end.
• As an aside, it may be of interest to some readers to consider how this addition table
can be implemented in the computer using only Boolean logic, without performing any
actual arithmetic.
• The result bit (the bit in the column that corresponds to the inputs) can be represented
by the EXCLUSIVE-OR function of the two input bits.
• The EXCLUSIVE-O‘ futio has a 1 as output oly if either iput, ut ot oth inputs,
is a 1.
• Siilarly, the arry it is represeted as a AND futio o the two iput its. 1 as
output if ad oly if oth iputs are a 1.
• This approach is discussed in more detail in Supplementary.
• The process of multiplication can be reduced conceptually to multiple additions, so it
should not surprise you that multiplication tables in different number bases are also
reasonably straightforward.
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