Entity-Relationship diagram: Entity-Relationship (ER) diagram is the method to represent the relational database using graphical form. This graphical representation shows only primary elements such as records, types, attributes, relationships between entities, and so on. The graphical representation of the ER diagram clearly describes the relationship among entities. In the diagram, every connector is labeled. On one side it is represented by the value 1, and on the other side it is labeled with the value “M”. This labeling is referred to as “cardinality constraint” of the relationship.

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2. Signed Integers Unsigned binary numbers work for natural numbers, but many calculations use negative numbers as well. To deal with this, a number of different methods have been used to represent signed numbers, but we will focus on two's complement, as it is the standard solution for representing signed integers. 2.1 Two's complement • Most significant bit has a negative value, all others are positive. So, the value of an n-digit -2 two's complement number can be written as: Σ2 2¹ di 2n-1 dn • Otherwise exactly the same as unsigned integers. i=0 - • A neat trick for flipping the sign of a two's complement number: flip all the bits (0 becomes 1, or 1 becomes 0) and then add 1 to the least significant bit. • Addition is exactly the same as with an unsigned number. 2.2 Exercises For questions 1-3, answer each one for the case of a two's complement number and an unsigned number, indicating if it cannot be answered with a specific representation. 1. (15 pts) What is the largest integer…

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Chapter 6, Problem 3PE

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Entity-Relationship diagram:

Entity-Relationship (ER) diagram is the method to represent the relational database using graphical form.

This graphical representation shows only primary elements such as records, types, attributes, relationships between entities, and so on.

The graphical representation of the ER diagram clearly describes the relationship among entities.

In the diagram, every connector is labeled.

On one side it is represented by the value 1, and on the other side it is labeled with the value “M”. This labeling is referred to as “cardinality constraint” of the relationship.

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2. Signed Integers Unsigned binary numbers work for natural numbers, but many calculations use negative numbers as well. To deal with this, a number of different methods have been used to represent signed numbers, but we will focus on two's complement, as it is the standard solution for representing signed integers. 2.1 Two's complement • Most significant bit has a negative value, all others are positive. So, the value of an n-digit -2 two's complement number can be written as: Σ2 2¹ di 2n-1 dn • Otherwise exactly the same as unsigned integers. i=0 - • A neat trick for flipping the sign of a two's complement number: flip all the bits (0 becomes 1, or 1 becomes 0) and then add 1 to the least significant bit. • Addition is exactly the same as with an unsigned number. 2.2 Exercises For questions 1-3, answer each one for the case of a two's complement number and an unsigned number, indicating if it cannot be answered with a specific representation. 1. (15 pts) What is the largest integer…

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1. Unsigned Integers If we have an n-digit unsigned numeral dn-1d n-2...do in radix (or base) r, then the value of that numeral is n−1 r² di Σi=0 which is basically saying that instead of a 10's or 100's place we have an r's or r²'s place. For binary, decimal, and hex r equals 2, 10, and 16, respectively. Just a reminder that in order to write down a large number, we typically use the IEC or SI prefixing system: IEC: Ki = 210, Mi = 220, Gi = 230, Ti = 240, Pi = 250, Ei = 260, Zi = 270, Yi = 280; SI: K=103, M = 106, G = 109, T = 10¹², P = 1015, E = 10¹8, Z = 1021, Y = 1024. 1.1 Conversions a. (15 pts) Write the following using IEC prefixes: 213, 223, 251, 272, 226, 244 21323 Ki8 Ki 223 23 Mi 8 Mi b. (15 pts) Write the following using SI prefixes: 107, 10¹7, 10¹¹, 1022, 1026, 1015 107 10¹ M = 10 M = 1017102 P = 100 P c. (10 pts) Write the following with powers of 10: 7 K, 100 E, 21 G 7 K = 7*10³