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Number Systems and Number Representation - Princeton …

Number Systems and Number Representation 1 2 For Your Amusement Question: Why do computer programmers confuse Christmas and Halloween? Answer: Because 25 Dec = 31 Oct -- 3 Goals of this Lecture Help you learn (or refresh your memory) about: The binary, hexadecimal, and octal Number Systems Finite Representation of unsigned integers Finite Representation of signed integers Finite Representation of rational numbers (if time) Why? A power programmer must know Number Systems and data Representation to fully understand C s primitive data types Primitive values and the operations on them Agenda Number Systems Finite Representation of unsigned integers Finite Representation of signed integers Finite Representation of rational numbers (if time) 4 5 The Decimal Number system Name decem (Latin) => ten Characteristics Ten symbols 0 1 2 3 4 5 6 7 8 9 Positional 2945 2495 2945 = (2)

Adding Unsigned Integers Addition Results are mod 24 23 11 7 0111 B + 10 + 1010 B-- ---- 1 10001 B 1 3 0011 B + 10 + 1010 B-- ---- 13 1101 B Start at right column ... Shifting Unsigned Integers Bitwise right shift (>> in C): fill on left with zeros Bitwise left shift (<< in C): fill on right with zeros Results are mod 24 25

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Congruence and Congruence Classes - Oklahoma State …

math.okstate.edu

notion of equality among the set of integers is an example of an equivalence relation. The next de nition yields another example of an equivalence relation. Definition 11.2. Let a;b;n 2Z with n > 0. ... Adding these two equations yields a c = n(k + k0) ; and so a c (mod n). 38. 11. CONGRUENCE AND CONGRUENCE CLASSES 39 Theorem 11.4. If a b (mod ...

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eprint.iacr.org

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