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lecture_08_RepNum_p2

# lecture_08_RepNum_p2 - Representation of Numbers and...

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1 Representation of Numbers and Precision There are 10 kinds of people in the world: people that understand binary, and people that don’t. Outline • Decimals • Binary Floating Point (IEEE 754)

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2 Representing Numbers • Decimal Roman Numerals Tally Marks • Binary Floating Point Decimal (Base10) 478.21 4x10 2 7x10 1 8x10 0 2x10 -1 1x10 -2
3 Decimal (Base10) 478.21 4 x10 2 + 7x10 1 + 8x10 0 + 2x10 -1 + 1x10 -2 digit Base10 Addition 79 + 25 79 + 25 104 1 79 + 25 4 1 carry

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4 Base10 Multiplication 79 x 25 395 + 158 0 10’s Placeholder 1975 Binary (Base2) 11011.11 1x2 4 1x2 3 0x2 2 1x2 1 1x2 0 1x2 -1 1x2 -2
5 Binary (Base2) 11011.11 1 x2 4 + 1x2 3 + 0x2 2 + 1x2 1 + 1x2 0 + 1x2 -1 + 1x2 -2 = 27.75 (base10) bit Binary (Base 2) There are 10 kinds of people in the world: people that understand binary, and people that don’t.

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6 Base2 Addition 1101 + 111 1101 + 111 0 0 1 1 1101 + 111 0 0 1 1 1 1 0 1 1101 + 111 0 1 carry Base2 Multiplication 1101 x 111 1101 1011011 1101 0 10’s placeholder + 1101 00 100’s placeholder 13 x 7 = 91
7 Finite Representation & Floating Point (IEEE 754) • Binary Limited range and precision.

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lecture_08_RepNum_p2 - Representation of Numbers and...

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