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Integers. Integer Storage Since Binary consists only of 0s and 1s, we cant use a negative sign ( - ) for integers. Instead, the Most Significant Bit is.

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Presentation on theme: "Integers. Integer Storage Since Binary consists only of 0s and 1s, we cant use a negative sign ( - ) for integers. Instead, the Most Significant Bit is."— Presentation transcript:

1 Integers

2 Integer Storage Since Binary consists only of 0s and 1s, we cant use a negative sign ( - ) for integers. Instead, the Most Significant Bit is used to represent the sign. This way, half the combinations in a fixed length of bits can be used to represent negative values. But which value of the sign bit (0 or 1) will represent a negative number?

3 Integers 2s Complement Notation

4 2s Complement Notation (examples in 8 bits to save space) Fixed length notation system. Uses 1 to represent negative values. The largest non-negative value: The smallest non-negative value: The largest negative value is: The smallest negative value is:

5 2s Complement Notation The representations of non-negative integers in 2s Complement look the same as they do for Natural numbers. However, negative values look VERY different than we might expect.

6 2s Complement Notation Complementary numbers sum to 0. Decimal is a Signed Magnitude system so complements have the same magnitude but different signs: 5 and -5, for example. 2s Complement is a Fixed Length system. There are no signs, so to find a numbers complement, another technique is needed.

7 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1.

8 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5:

9 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length

10 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length

11 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length flip the bits ( 1 0, 0 1 )

12 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length flip the bits ( 1 0, 0 1 )

13 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length flip the bits ( 1 0, 0 1 ) add 1 to the new pattern+1

14 2s Complement Notation One such technique is to simply change each bit to its opposite, and then add 1. To find the 2s complement notation for -5: Represent +5 in fixed length flip the bits ( 1 0, 0 1 ) add 1 to the new pattern+1 to produce

15 2s Complement Notation Complementary numbers sum to 0.

16 2s Complement Notation Complementary numbers sum to 0. So if to

17 2s Complement Notation Complementary numbers sum to 0. So if to +5 we add

18 2s Complement Notation Complementary numbers sum to 0. So if to +5 we add -5 we should get discard the carry bit to retain the fixed length


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