Tags |
|
|
Links |
|
|
Casual Articles - History of the Computer - Negative Numbers for Subtraction
There are a handful of characteristics successful entrepreneurs possess. The degree to which you have these skills will certainly influence your ability to succeed in a business of your own. Of all the characteristics entrepreneurs have, one that certainly stands tall is the ability to make decisions including those that involve risk. After all the very nature of a true entrep
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition
Human beings are prone to injury of some kind or other. These may be mental or physical injuries. When a person’s action injures the individual and family mentally or physically, it is called Personal Injury. The individual can file a case against the person who has been the cause of his or her Personal Injury.For instance, in a car accident an individual is left paraly
To form a negative number, we simply invert the positive number, in binary, and add 1. For example
0000 0110 - (6) inverted becomes
1111 1001 - now add 1 to get
1111 1010 - (-6)
This is how a computer records -6. The Most Significant Bit - in this case bit 7 or bit value 128 decimal is used as the Sign Bit. If this bit is a zero, the number is positive, if it is a one, the number is negative. This notation is known as 'Twos Complement'.
(There is also 'Ones Complement', without the added 1, which was used in some proprietary systems, but it required more complicated logic to get around problems like having + and - zero. It is not necessary to go into the detail of this notation for an understanding of the logic.)
The Sign bit uses one of the bit positions, meaning that our range of numbers is reduced. For example 0111 1111 is the highest positive 8-bit number (127 decimal). The next number, 128 decimal would be 1000 0000, however the bit value 128 in bit 7 cannot be used as it is now the sign bit.
SUBTRACTION
Now we can have a negative number it will be easy to subtract. We can use an adder, which we already have. This is possible because 9-3 is the same as 9+(-3). For instance 9-3 decimal is 00001001-00000011 in 8 bit binary. We take the 9 and add it to the twos complement of 3, thus we can use our adder with a bit of extra logic to invert the negative number and add 1 to it. The twos complement of 3 (decimal) or in binary
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition?
Can you write a joke? Starting from an existing joke might help. We’ll give it a try with five bar jokes. I’ve condensed these from Aha Jokes.* Here we go!Existing Bar Joke #1A man is drinking in a bar when a nun harasses him about drinking. In self-defense the man says, “Who told you that drinking is bad?” Nun: Mother Superior told me. Man: So, have y
This is how a computer records -6. The Most Significant Bit - in this case bit 7 or bit value 128 decimal is used as the Sign Bit. If this bit is a zero, the number is positive, if it is a one, the number is negative. This notation is known as 'Twos Complement'.
(There is also 'Ones Complement', without the added 1, which was used in some proprietary systems, but it required more complicated logic to get around problems like having + and - zero. It is not necessary to go into the detail of this notation for an understanding of the logic.)
The Sign bit uses one of the bit positions, meaning that our range of numbers is reduced. For example 0111 1111 is the highest positive 8-bit number (127 decimal). The next number, 128 decimal would be 1000 0000, however the bit value 128 in bit 7 cannot be used as it is now the sign bit.
SUBTRACTION
Now we can have a negative number it will be easy to subtract. We can use an adder, which we already have. This is possible because 9-3 is the same as 9+(-3). For instance 9-3 decimal is 00001001-00000011 in 8 bit binary. We take the 9 and add it to the twos complement of 3, thus we can use our adder with a bit of extra logic to invert the negative number and add 1 to it. The twos complement of 3 (decimal) or in binary
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition
The average man in the street assumes that Life Insurance and Life Assurance are names for the same form of insurance. How wrong they are! But don't hang your head in shame, many financial commentators get it wrong too! Life Insurance and Life Assurance perform different financial roles and are poles apart in cost - so it helps to surf for the correct product.
The Sign bit uses one of the bit positions, meaning that our range of numbers is reduced. For example 0111 1111 is the highest positive 8-bit number (127 decimal). The next number, 128 decimal would be 1000 0000, however the bit value 128 in bit 7 cannot be used as it is now the sign bit.
SUBTRACTION
Now we can have a negative number it will be easy to subtract. We can use an adder, which we already have. This is possible because 9-3 is the same as 9+(-3). For instance 9-3 decimal is 00001001-00000011 in 8 bit binary. We take the 9 and add it to the twos complement of 3, thus we can use our adder with a bit of extra logic to invert the negative number and add 1 to it. The twos complement of 3 (decimal) or in binary
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition
When you decide to start a small business, you find out pretty quickly that it takes more than skills and dedication in your respective area of work. Besides being good at what you want to do, you also need to known your accounting and financing issues, no matter how annoying and boring these may be. And the credit card problem for small businesses needs careful handling, just
SUBTRACTION
Now we can have a negative number it will be easy to subtract. We can use an adder, which we already have. This is possible because 9-3 is the same as 9+(-3). For instance 9-3 decimal is 00001001-00000011 in 8 bit binary. We take the 9 and add it to the twos complement of 3, thus we can use our adder with a bit of extra logic to invert the negative number and add 1 to it. The twos complement of 3 (decimal) or in binary
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition
Because of corporate downsizing, many people have been laid-off or voluntarily taken early retirement packages and/or incentives. This happens when times are good due to mergers and acquisitions or when the economy is in the dumps and corporations are working to cut payroll costs. Almost all of these people have absolutely had it with corporate life; they feel burned and unap
of 0000 0011
is 1111 1100
add 1 + 0001
is 1111 1101
Now add to the 9 (decimal) using an 8 bit adder:-
7654 3210 - bit #
0000 1001 - (9)
1111 1101 - (-3)
Remember your binary addition?
Least significant bit (bit 0), 1+1 is 0 and a carry.
Next bit (bit 1) is 0+0+carry = 1 no carry.
Next bit (bit 2) is 1+0 = 1 no carry.
Next bit (bit 3) is 1+1 = 0 and a carry.
Next bit (bit 4) is 1+0+carry = 0 and a carry.
Next 3 bits (5,6,7) are the same as 4 - 1+0+carry = 0. The last carry falls off the end.*
So we get:-
0000 0110 (6 Decimal - 9-3=6)
Which, fortunately, if you followed it, is the right answer! Are these computers smart or what? This system works with negative results as well, for instance try 3-9. You should end up with the twos complement of 6. This is not a compulsory exercise!
* The carry from the most significant bit, in this example bit 7, but could be bit 31 or 63 in some computers, is ignored in this case. However it is used in some functions, for instance a circular bit shift, which we will look at in a later article.
HTTP = HTML link (for blogs, profiles,phorums):
<a href="http://www.casualarticles.com/article/176869/casualarticles-History-of-the-Computer--Negative-Numbers-for-Subtraction.html">History of the Computer - Negative Numbers for Subtraction</a>
BB link (for phorums):
[url=http://www.casualarticles.com/article/176869/casualarticles-History-of-the-Computer--Negative-Numbers-for-Subtraction.html]History of the Computer - Negative Numbers for Subtraction[/url]
Related Articles:
Innovative Industrial Name Plates For Your Brand Establishment
How To Find A Job In The Hidden Job Market
Bookmark it:
|