Unit 1: Exam Review Notes
Collaboration and Teamwork
Teamwork: Primarily focuses on individuals getting along and working together harmoniously.
Collaboration: A deeper process that involves:
Creating new understandings for a problem or task.
Embracing disagreement and finding ways to combine opposing points of view.
Going beyond passively agreeing; avoiding conflict may hinder genuine collaboration.
Requiring participants from diverse backgrounds and with varied perspectives to foster richer solutions.
Bits and Bytes: Fundamentals of Digital Information
Bit: The most basic unit of information, representing either a 0 or a 1.
Byte: A unit of digital information comprising 8 bits.
An 8-bit system (1 Byte) is capable of storing values up to 255.
It can represent a total of 256 unique number options, including 0.
Binary Number Operations
Sequential ID Assignment
Problem: If student IDs increase sequentially by 1, and the last ID assigned was binary 1001 hinspace 0011, what is the next ID?
Solution Steps:
Convert the given binary to decimal: (1001 hinspace 0011)2 = (1 \cdot 2^7) + (0 \cdot 2^6) + (0 \cdot 2^5) + (1 \cdot 2^4) + (0 \cdot 2^3) + (0 \cdot 2^2) + (1 \cdot 2^1) + (1 \cdot 2^0) = 128 + 0 + 0 + 16 + 0 + 0 + 2 + 1 = 147{10}.
Add 1 to the decimal value: 147 + 1 = 148_{10}.
Convert the new decimal value back to binary:
Find the largest power of 2 less than or equal to 148 (128 = 2^7).
Subtract 128 from 148 (remainder 20).
Next power of 2 less than 20 is 16 = 2^4.
Subtract 16 from 20 (remainder 4).
Next power of 2 less than 4 is 4 = 2^2.
Subtract 4 from 4 (remainder 0).
The binary representation is formed by placing a 1 at the positions corresponding to the powers of 2 used, and 0 otherwise: 1001 hinspace 0100_2.
Answer: The next ID will be binary 1001 hinspace 0100.
Ordering Numeric Values
Problem: Order the following values from least to greatest: Binary 1011, Binary 1101, Decimal 5, Decimal 12.
Solution Steps:
Convert all binary numbers to decimal for consistent comparison:
(1011)2 = (1 \cdot 2^3) + (0 \cdot 2^2) + (1 \cdot 2^1) + (1 \cdot 2^0) = 8 + 0 + 2 + 1 = 11{10}.
(1101)2 = (1 \cdot 2^3) + (1 \cdot 2^2) + (0 \cdot 2^1) + (1 \cdot 2^0) = 8 + 4 + 0 + 1 = 13{10}.
List all values in decimal: 5, 11, 12, 13.
Order them from least to greatest:
5 (Decimal)
11 (Binary 1011)
12 (Decimal)
13 (Binary 1101)
Answer: Decimal 5, binary 1011, decimal 12, binary 1101.
Data Representation Errors
Fixed Number of Bits: Computers represent numbers using a fixed number of bits, which limits the range and precision of values that can be stored.
Overflow Error: Occurs when a computer attempts to represent a number that is too large for the allocated number of bits.
Example 1: With 8 bits:
Maximum representable value is 2^8 - 1 = 255.
The smallest number that would cause an overflow error is 256.
Example 2: With 6 bits:
Maximum representable value is 2^6 - 1 = 63.
The smallest number that would cause an overflow error is 64.
Hint: An overflow error is caused by the numerical value that would require the
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