Complements Essay
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COMPLEMENTS
INTRODUCTION:
Basic binary digits are described as UNSIGNED values. This is because if you
look at the string of bits (zeros and ones) there is no indicator whether or
not this value is positive or negative. You must use an additional symbol "+"
or "-" to indicate the sign of the number. There are some types of number
systems where you can determine the sign of number without using an addition
symbol. You can tell whether it is positive or negative by looking at the
bits. Such representations are referred as SIGNED representations because you
can determine the sign of the number from the number itself.
In signed representations you the MOST SIGNIFICANT BIT (MSB) indicates the sign
of the number. The MSB is the left most bit. If the MSB is equal to 0 then the
number is positive. If the MSB is equal to 1 then the number is negative.
e.g. 001111101 is positive
^
|
The MSB is equal to zero
e.g. 101101010 is negative
^
|
The MSB is equal to one
At this point you might ask yourself why bother with signed representations -
we perform decimal based subtractions in every day life using base ten
unsigned representations and we're all happy and well adjusted people. The
reason why it's important to learn about signed representations is because
when the computer tries to subtract one number Y from another number X, it
doesn't do so in the same way that we do: i.e X - Y
Instead it uses a technique known as negating and adding:
i.e. X + (-Y) which is still equal to X - Y
CONVERSIONS (UNSIGNED BINARY TO SIGNED VALUES)
This is summary of what you must do to convert an unsigned binary value to a
complemented value.
1's complement 2's complement
Binary value >= 0 No change No change
Binary value < 0 Swap the bits Swap the bits and add
one to the result.
Carry out? Add it back in Ignore it
Swapping the bits means we substitue 1's for 0's and 0's for 1's.
DOING SUBTRACTIONS VIA COMPLEMENTS (ala Negate and Add)
How do we do this with the negate and add? First convert these numbers to
binary:
Base 10 Base 2 (must be signed!)
eg 4 0100
-6 -0110*
= -2
*I added one extra zero to the left hand...
MLA Style
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