Binary, Octal, Hexadecimal Conversion Quiz

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Questions and Answers

What are the four main types of number systems mentioned in the text?

Binary, Octal, Decimal, Hexadecimal

How many digits does the binary number system use?

What is the base of the octal number system?

What kind of data is stored in terms of bits and bytes in computers?

The data in computers Signup and view all the answers

What is the 1's complement of the binary number 100101?

011010 Signup and view all the answers

Convert the octal number 345 to hexadecimal.

E5 Signup and view all the answers

Perform a binary addition of 1011 and 1101.

11000 Signup and view all the answers

Convert the hexadecimal number B4 to octal.

266 Signup and view all the answers

What is the 2's complement of a binary number?

The 2's complement of a binary number is obtained by adding 1 to the Least Significant Bit (LSB) of 1's complement of the number. Signup and view all the answers

How is binary subtraction different from binary addition?

Binary subtraction involves borrowing when the minuend is smaller than the subtrahend, while binary addition does not have this concept of borrowing. Signup and view all the answers

What are the basic rules for binary subtraction?

The basic rules for binary subtraction are: 0–0=0, 1–1=0, 1–0=1, and 0–1=1 with a transfer (borrow) of 1. Signup and view all the answers

Describe the process of binary division and how it compares to division in the decimal system.

Division in the binary number system employs the same procedure as division in the decimal system. Both systems follow similar steps to perform division. Signup and view all the answers

What are the digits used in the decimal number system?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Signup and view all the answers

What is the base number of the hexadecimal number system?

16 Signup and view all the answers

How are the alphabets A-F in the hexadecimal system related to the decimal system?

A-F in the hexadecimal system represents the numbers 10-15 in the decimal system, respectively. Signup and view all the answers

What is the purpose of using the hexadecimal number system in computers?

It is used to reduce the large-sized strings of the binary system. Signup and view all the answers

Study Notes

Number Systems

Four main types of number systems:
- Decimal
- Binary
- Octal
- Hexadecimal

Binary System

Binary number system uses only two digits: 0 and 1.

Octal System

Base of the octal number system is 8, using digits from 0 to 7.

Data Storage in Computers

Data is stored in computers using bits (0 or 1) and bytes (8 bits), representing the smallest units of data.

1's Complement

The 1's complement of the binary number 100101 is 011010.

Octal to Hexadecimal Conversion

The octal number 345 converts to hexadecimal as B5.

Binary Addition

Performing binary addition of 1011 and 1101 results in 11000.

Hexadecimal to Octal Conversion

The hexadecimal number B4 converts to octal as 264.

2's Complement

The 2's complement of a binary number is found by inverting the bits and adding 1 to the least significant bit.

Binary Subtraction

Binary subtraction differs from binary addition in that it involves borrowing when the minuend is smaller than the subtrahend.

Basic Rules of Binary Subtraction

If subtracting 0 from 0 or 1 from 1, the result is 0.
Subtracting 1 from 0 requires borrowing from the next left bit.

Binary Division Process

Binary division involves repeated subtraction and multiplication, analogous to decimal division but employs binary values (0 and 1) only.

Decimal System Digits

The decimal number system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hexadecimal System

The base number of the hexadecimal system is 16, incorporating digits from 0 to 9 and letters A to F.

Hexadecimal and Decimal Relationship

Alphabets A-F in hexadecimal correspond to decimal values 10-15 respectively.

Purpose of Hexadecimal

The hexadecimal number system is used in computers for a more compact and human-readable representation of binary values, simplifying coding and debugging.

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Description

Test your knowledge of converting between binary, octal, and hexadecimal numbers to decimal, as well as the reverse conversion. Practice using multiplication and addition methods for conversion and familiarize yourself with conversion tables for octal and hexadecimal to binary and vice versa.