Computer Science - 4CP0 PearsonEdexcel

Binary

Overview

A computer's processor only ever switches between two electrical states, and everything it stores or calculates has to be built out of those two states. Numbers, letters, photographs and even the instructions of the program itself are all, deep down, patterns of binary digits.

In this lesson you will learn to convert confidently between binary, denary and hexadecimal, add two binary numbers and recognise when the result overflows an 8-bit register, shift a binary pattern left and right, and represent both positive and negative whole numbers using sign-and-magnitude and two's complement.

Objectives

Understand that computers use binary to represent data (numbers, text, sound, graphics) and program instructions
Understand how computers represent and manipulate numbers (unsigned integers, signed integers (sign and magnitude, two's complement))
Be able to convert between binary and denary whole numbers (0-255)
Understand how to perform binary arithmetic (add, shifts (logical and arithmetic)) and understand the concept of overflow
Understand why hexadecimal notation is used and be able to convert between hexadecimal and binary

Lesson Note

A computer's circuits are built from switches that are only ever fully on or fully off; there is no reliable middle state to detect at high speed. Binary, the base-2 number system using only the digits 0 and 1, maps perfectly onto this: 1 for on, 0 for off. Every kind of data a computer handles, whole numbers, text, sound, images and even the program instructions themselves, is ultimately stored as a pattern of these binary digits (bits), just interpreted differently depending on what it represents.

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Lesson Evaluation

Congratulations on completing the lesson on Binary. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

What is the denary value of the 8-bit binary number 00110010? A) 48 B) 50 C) 52 D) 56 Answer: B
How many bits are grouped together to form a single hexadecimal digit? A) 2 B) 3 C) 4 D) 8 Answer: C
An 8-bit unsigned register adds 250 and 10. What happens? A) The result 260 is stored correctly B) Overflow occurs and the stored result is incorrect C) The register automatically becomes 16-bit D) The addition is rejected and nothing is stored Answer: B
Which type of shift copies the sign bit into new positions created by a right shift? A) Logical shift B) Arithmetic shift C) Circular shift D) Hexadecimal shift Answer: B
In two's complement, what does the leftmost bit of an 8-bit number represent? A) A place value of +128 B) A place value of -128 C) Always 0 D) The number of bits used Answer: B