Worksheet: 9th Computer Science |chapter-2| Lecture 2|Top:Data Representation |PCTB|2025-26

Worksheet: 9th Computer Science |chapter-2| Lecture 2|Top:Data Representation |PCTB|2025-26

JaxDoc

Number System Lecture 2 | Data Representation in Computing Systems | Binary Encoding of Integers

Vocabulary

Binary Encoding — The process of representing data, especially numbers, using a binary (base-2) system, typically with 0s and 1s.
Integer (Z) — Whole numbers, including positive, negative, and zero. In computing, these are often referred to as signed integers when both positive and negative values are represented.
Whole Numbers (W) — A set of non-negative integers, including zero and all positive integers (0, 1, 2, 3, …).
Sign Bit — A reserved bit in a binary representation of a number that indicates whether the number is positive (0) or negative (1).
Two’s Complement — A method used by computers to represent and store negative numbers, involving inverting all bits and then adding one.

Questions

Watch the video and answer the following questions based on the information presented.

According to the video, what is the maximum positive value that can be stored in a 1-byte whole number (8 bits)?

The video demonstrates converting the decimal number -5 to an 8-bit binary number using two’s complement. What are the two main steps involved in this conversion?

What is the minimum value that can be represented by a 2-byte signed integer, as stated in the video?

In the context of binary encoding for integers, what does the sign bit (the most significant bit) indicate if it is ON (1)?

The value is positive.
The value is zero.
The value is negative.
The value is undefined.

Explain why understanding how integers are stored in memory, including concepts like whole numbers, signed integers, and two’s complement, is important for computer science students and programmers. Provide at least two reasons based on the video’s discussion.