The binary number system

Binary Basics

100

What is a binary number?

A binary number is a number expressed in the base-2 numeral system, which uses only two digits: 0 and 1.

200

What is the base of the binary system?

The base of the binary system is 2.

300

What is the significance of '0' and '1' in binary?

In binary, 0 represents the "off" state, and 1 represents the "on" state, which is used to represent data and instructions in digital systems.

400

What is a byte?

A byte is a unit of digital information that consists of 8 bits.

500

What is a bit?

A bit (binary digit) is the smallest unit of data in a computer, representing a single binary value of 0 or 1.

Conversion Techniques

100

Convert 1010 to denary.

• 1010 in binary is 10 in decimal (denary).

200

Convert 1111 to denary.

15

300

Convert 100110 to denary.

100110 in binary is 38 in decimal.

400

Convert 255 to binary.

255 in decimal is 11111111 in binary.

500

Convert 64 to binary.

64 in decimal is 1000000 in binary.

Binary Arithmetic

100

What is 101 + 110 in binary?

• 101 + 110 in binary is 1011.

200

What is 1001 - 0011 in binary?

1001 - 0011 in binary is 0110 (or just 110).

300

What is 110 * 10 in binary?

110 * 10 in binary is 1100.

(It's 6 multiplied by 2)

400

What is 1010 divided by 10 in binary?

1010 ÷ 10 in binary is 101.

(it's 10 divided by 2)

500

What is the result of 1110 + 1011 in binary?

1110 + 1011 in binary is 11001.

Applications of Binary

100

Name one device that uses binary.

• Computers (or any digital device, like smartphones).

200

What is ASCII and how does it relate to binary?

• ASCII (American Standard Code for Information Interchange) is a character encoding standard that represents text using binary numbers, typically using 7 or 8 bits per character.

300

How is binary used in computer networking?

Binary is used to represent data transmitted over a network, including IP addresses, MAC addresses, and the data in packets. Everything is broken down into binary bits.

400

How does binary relate to image file sizes?

Image file sizes are determined by the number of bits used to store each pixel's color information. The more bits used, the larger the file size.

500

Describe how binary is used in programming languages.

Binary is the foundation of all programming languages. High-level code written in languages like Python, Java, or C++ is compiled or interpreted into binary machine code that a computer's CPU can execute.

Fun Facts about Binary

100

How many digits are in a binary number?

• A binary number can have any number of digits. Each digit in a binary number is called a bit.

200

What is the highest binary digit?

The highest binary digit is 1.

300

What year was the binary system first introduced?

The modern binary system was introduced by Gottfried Wilhelm Leibniz in 1703.

400

What is the binary representation of the decimal number 10?

The binary representation of 10 is 1010.

500

How would you find the double of any binary number without performing any calculations?

Shift the bits to the left, in other words add a 0 to the end.

Eg : 1010 ----> 10100

Try it yourself!