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Slide 1

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Binary Arithmetic, For idiots
Bradley Mangham…read more

Slide 2

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Addition is the easiest of the arithmetic functions in binary.
There are a few simple rules to adhere by:
- 0+1 = 1
- 1+1 = 0 carry 1
- 1+1+1 = 1 carry 1
If the carrying leads to the new binary number being larger that the two being added, it is called an
overflow error, and we discount the `overflowed' digit.…read more

Slide 3

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Subtraction can be done in a couple of ways, but I will focus on the main one used. Unfortunately,
this is the hardest.
Again there are a few rules to do this:
- 1-1 = 0
- 1-0 = 1
- 0-1 = Carry 1 up to zero, making 10 - 1 = 1. Then add 1 to the second number on the next
significant bit.…read more

Slide 4

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Subtraction By Two's Complement
Subtraction by Two's Complement is a much easier method of subtraction, however you can only use
it if specified. The rules go as follows:
- Convert the number to be subtracted into a negative two's compliment number
- Add them…read more

Slide 5

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Converting Exponent and Mantissa to Denary
Converting binary numbers split into an exponent and a mantissa is hard.
What we first do, is write out our mantissa, and place a decimal point after the MSB, without giving
any of the digits a value. We then evaluate the value of the exponent. Depending on the value of the
exponent, we move the decimal place on the mantissa. For example, if the exponent was equal to 1,
we would move the decimal place 1 point. We then add the values to the mantissa and evaluate in
denary.…read more

Slide 6

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Converting Exponent and Mantissa to Denary Cont.
Take this example:
0 1 1 0 0 0 0 1
The mantissa is 01100 and the exponent is 001. We know that the value of the exponent is 1. We
therefore move the decimal place one place to the right.
-2 1 ½ ¼
0 1 1 0 0
The mantissa and exponent are always in Two's complement form. After moving the decimal place
we can add the values and evaluate the denary equivalent, which is 1.5…read more

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