Binary

Lesson: Introduction to Binary Numbers

Objective: By the end of this lesson, you will be able to understand what binary numbers are, convert binary numbers to decimal (base-10) numbers, and vice versa.

What are Binary Numbers?

Binary numbers are a base-2 numbering system. Unlike our everyday decimal (base-10) system, which uses ten digits (0-9), binary only uses two digits: 0 and 1. This system is fundamental in computer science and digital electronics, as computers use binary digits (bits) to represent data and perform calculations.

Converting Decimal to Binary:

To convert a decimal number to binary, you repeatedly divide the decimal number by 2, keeping track of the remainders. The remainders, read from bottom to top, give the binary representation

Convert the binary number 11001 to decimal.

1. 17
2. 18
3. 25
4. 27

Convert the binary number 1011 to decimal.

1. 5
2. 7
3. 10
4. 13

Convert the binary number 1001 to decimal.

1. 6
2. 8
3. 9
4. 10

Convert the binary number 11100 to decimal.

1. 12
2. 28
3. 16
4. 20

Convert the decimal number 29 to binary.

1. 11111
2. 11110
3. 11101
4. 11100

Convert the decimal number 51 to binary.

1. 110011
2. 110100
3. 110101
4. 110110

Convert the binary number 101010 to decimal.

1. 42
2. 32
3. 48
4. 40

Convert the decimal number 12 to binary.

1. 1010
2. 1100
3. 1110
4. 1111

Convert the decimal number 15 to binary.

1. 1000
2. 1100
3. 1110
4. 1111

Example 1: Convert 13 to Binary:

13 ÷ 2 = 6 remainder 1

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 1101

Example 2: Convert 28 to Binary:

28 ÷ 2 = 14 remainder 0

14 ÷ 2 = 7 remainder 0

7 ÷ 2 = 3 remainder 1

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 11100

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