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| A mathematical concept; E.g.: Natural numbers, integers, reals, rationals |
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| Used to represent a number |
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| Computer is a _____ _____ system |
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| Discrete; finite number of symbols; opposite is _____ (continuous) |
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| (Base two); 2 symbols/states/values; 0 and 1 (or letters 'O' and 'I') |
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| Basic unit of information, also called the binary digit |
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| n bits -> _____ possible states |
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| Operates by controlling the flow of electrons |
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| _____ data, simply means an agreed upon _____ of data from one representation to another |
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| 27=128 combinations; standard encoding, developed in the 1960s, didn't take into account international standards |
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| ASCII (American Standard Code for Information Interchange) |
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| 8-bit encoding, 28=256 possibilities |
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| What is the most and least significant digit in 101? |
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| Radix-10: _____ Radix 2: _____ Radix 16: _____ |
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| Use k symbols- also known as k-ary numbers |
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| How many different radix k numbers of length n? |
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What does this algorithm do?
//input is Decimal number N, output is list of bits bi
i=0;
while N>0
do bi=N%r; //bi=remainder; N mod r
N=N/r; //N becomes quotient of division i++;
end while |
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| Computes the base r representation for N |
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| When operation result is outside type's range |
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| The sum of 2 n-bit numbers can have _____ bits |
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| The product of 2 n-bit numbers can have _____ bits |
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| Architecture remembers overflow (carry-out) bit |
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| Overflow: Architecture stores upper n-bits in register. Can use these if you want. |
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| In a computer memory each storage location can only hold a _____ number of bits |
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| If we use an n-bit storage location to store a 'regular' unsigned number we can store numbers between 0 and _____ inclusive. |
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| What negative representation are these? 00101=5 10101=-5 00101=5 11010=-5 |
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| sign-magnitude, 1's Complement |
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| Range of Signed Magnitude, 1's Complement, 2's Complement |
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| -2N-1+1<i<2N-1-1, -2N-1+1<i<2N-1-1, -2N-1<i<2N-1-1 |
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| To represent a number X we actually compute and store (2n+X) |
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| Advantages of _____ _____- operations need not check the sign, only 1 representation for zero, efficient use of all the bits |
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| Arithmetic Overflow: Any addition that produces an 'extra bit' is a problem; Sometimes addition or subtraction produce an extra bit- this is not necessarily a problem, Arithmetic overflow can occur when you are adding 2 positive or 2 negative numbers- in this case if the sign of the result is _____ from the sign of the addends you have an arithmetic overflow |
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| Unsigned numbers, 2's Complement signed numbers, different |
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| 2's Complement Pencil-and-Paper Shortcut: Copy bits from _____ to _____ up to and including the first _____. _____ remaining bits. |
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Converting Decimal to Binary (2's C)
1. Find magnitude of decimal number. (Always _____.)
2. Divide by _____ - remainder is _____ significant bit.
3. Keep dividing by 2 until answer is _____, writing remainders from _____ to _____.
4. Append a _____ as the _____ bit; if original number was _____, take 2's Complement. |
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| positive, 2, least, 0, right, left, 0, MS, negative |
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| To add 2 different sized bits, pad the smaller sized bits on the _____ with the _____ bit. |
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