Mathematics | Class: JSS1 | Term: 1st

Number Base System

len Alfred Ajibola - 01st February, 2026 @ 09:24 PM

Topics in Mathematics

Linear Equation in Mathematics Word Problems leading to Algebraic Expression BODMAS in Algebra Multiplication and Division in Algebra Addition and Subtraction in Algebra Multiplication of Number Bases Subtraction of Number Bases Addition of Number Bases Division of Number Base Number Base Conversion Number Base System Significant Figures Rounding Off Numbers Decimal Place Value Fraction Word Problems Word Problems in Fraction Multiplication and Division of Fractions Addition and Subtraction of Fractions Expressing One Quantity as a Percentage of Another Expressing One Quantity as a Fraction of Another


Academic Questions in Mathematics

Please click here to see all Questions and Answers

Decagon - Len Academy

What type of polygon is shown in the above image?

  • A. Nonagon

  • B. Decagon

  • C. Octagon

  • D. Hexagon

  • E. Hepagon

  • F. Pentagon

Which of the following is not part of a circle?

  • A. Section

  • B. Sector

  • C. Segment

  • D. Semicircle

  • E. Secant

  • F. Center

Acute Angle - Len Academy

What angle is shown in the above image?

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

An angle greater than 90o but less than 180o is termed _____.

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

Factorize 12a2 - 20a + 3

  • A. (6a - 1)(2a - 3)

  • B. (6a - 1)(2a + 3)

  • C. (6a + 1)(2a - 3)

  • D. (6a + 1)(2a + 3)

  • E. (-6a + 1)(2a - 3)

  • F. (-6a + 1)(2a + 3)

Simplify 10ab + 7ab

  • A. 17ab2

  • B. 17a2b2

  • C. 3ab2

  • D. 3a2b2

  • E. 17ab

  • F 3ab

Which of the following is not a type of angle?

  • A. Right angle

  • B. Left Angle

  • C. Acute Angle

  • D. Complete Angle

  • E. Straight Angle

  • F. Reflex angle

Two lines that can never meet each other are best considered as _____ lines.

  • A. straight
  • B. vertical
  • C. horizontal
  • D. parallel
  • E. oblique
  • F. perpendicular



Binary Number System (Base 2)


Binary number system, also known as Base 2 in mathematics uses two digits only, and that's: 0 and 1. These two digits, (0 and 1,) are called binary digits or simply "bits".

A binary number is often written with the subscript 2. For example, 100110 base 2 is written as 1001102.

Also, understand that the place value in base 2 system uses the powers of 2; that is; "ones, twos, fours, eights, sixteens, and so on". This is clearly different from the place value in base 10 where each position represents a power of 10; that is, "ones, tens, hundreds, thousands, etc."

Please read on the place value of numbers here.

 


Conversation of Base 2 (Binary) to Base 10 (Decimal) and vice versa


The conversion between binary to decimal is quite straightforward.

In order to convert a binary number to its decimal equivalent, three steps are needed.

  • Designate each digit from right to left with the digit position 0, 1, 2, 3, 4, 5 and so on. For example, in the binary digit "1001"; the 1 at the outermost right is designated wth a digit position of 0; the third zero with a digit position 1. The second zero with a digit position 2, and the first 1 with a digit position 3. This is further shown in the image below:

Binary place value for 1001 base 2 - Len Academy

  • We will multiply each digit in the binary by its corresponding power of 2.

  • Sum or Add our results above.

Please read on number base conversion here.

 

The conversion 10012 to base 10 is further explained below:

  • Note: The digit position is crucial in converting binary (or other bases) to base 10. In the case of 1001, the last 1 has a digit position of 0, the third zero has a digit position of 1, the second zero has a digit position of 2 and the first 1 has a digit position of 3. Once this is known, steps 2 and 3 above is followed.

(1 × 23) + (0 × 22) + (0 × 21) × (1 × 20)

8 + 0 + 0 + 1 = 910 or 9

Please read on the addition of number bases here.

 

In order to convert a decimal number to binary (or base 2), we'll repeatedly divide the decimal number by 2, keeping track of the remainders, until we attain a 'zero remainder one' value. Next, the binary representation is formed by reading the remainders from bottom to top (or in the reverse order of our division). Below is an example.

  • Convert 910  to base 2

9 ÷ 2 = 4 R 1

4 ÷ 2 = 2 R 0

2 ÷ 2 = 1 R 0

1 ÷ 2 = 0 R 1

The binary notation is derived from bottom to top and that's: 1001

Please read on the division of number bases here.

 


Worked Examples on Binary conversation to Base 10 and (from Base 10 to Binary)


Example 1
  • Convert 10112 to base 10

Solution 

(1 × 23) + (0 × 22) + (1 × 21) + (1 × 20)

  • 8 + 0 + 2 + 1 = 1110 or 11

 

Example 2
  • Convert 1112 to base 10

Solution 

(1 × 22) + (1 × 21) + (1 × 20)

  • 4 + 2 + 1 = 710 or 7

 

Example 3
  • Convert 100012 to base 10

Solution 

(1 × 24) + (0 × 23) + (0 × 22) + (0 × 21) + (1 × 20)

  • 16 + 0 + 0 + 0 + 7= 1710 or 17

 

Example 4
  • Convert 1110012 to base 10

Solution 

(1 × 25) + (1 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20)

  • 32 + 16 + 8 + 0 + 0 + 1 = 5710 or 57

 

Example 5
  • Convert 2410 to base 2

Solution 

24 ÷ 2 = 12 R 0

12 ÷ 2 = 6 R 0

6 ÷ 2 = 3 R 0

3 ÷ 2 = 1 R 1

1 ÷ 2 = 0 R 1

  • 110002

 

Example 6
  • Convert 43 to base 2

Solution 

43 ÷ 2 = 21 R 1

21 ÷ 2 = 10 R 1

10 ÷ 2 = 5 R 0

5 ÷ 2 = 2 R 1

2 ÷ 2 =1 R 0

1 ÷ 2 = 0 R 1

  • 1010112

 

Example 7
  • Convert 63 to base 2

Solution 

63 ÷ 2 = 31 R 1

31 ÷ 2 = 15 R 1

15 ÷ 2 = 7 R 1

7 ÷ 2 = 3 R 1

3 ÷ 2 =1 R 1

1 ÷ 2 = 0 R 1

  • 1111112

 

Example 8
  • Convert 100 to base 2

Solution 

100 ÷ 2 = 50 R 0

50 ÷ 2 = 25 R 0

25 ÷ 2 = 12 R 1

12 ÷ 2 = 6 R 0

6 ÷ 2 = 3 R 0

3 ÷ 2 =1 R 1

1 ÷ 2 = 0 R 1

  • 11001002

Please read on the subtraction of number bases here.

Please read on the multiplication of number bases here.

 


Assignment on Base 2 conversion to Base 10 ( and from Base 10 to Binary)


1. Convert the following to base 2

  • 99

  • 37

  • 132

  • 547

  • 311

  • 452

  • 88

  • 33

  • 1000

  • 2048

 

2. Convert the following from binary to decimal:

  • 101110

  • 10010111

  • 10101011

  • 10011

  • 1111

  • 11111100

  • 1101101101101101

  • 1000000

  • 100100

  • 101101

Please read on mathematics week 9 topic for jss1 first term here.

Please read on mathematics week 9 scheme of work for jss1 first term here.

Kindly share this article via the links below:


len


Please click here to contact Alfred if you require any of the following services:

  • If you need a standard website at an affordable price.

  • Online training on the academic subjects: biology, chemistry and basic science.

  • If you require an advanced smart school management system (web application) for your school.

Click here to read on Len Academy Smart School Software.


Please click here to follow Len Academy on Google News.



Amazing facts in Mathematics

The opposite sides of a dice will always give a sum of seven

31,556,926 seconds makes one year

From 0 through 1000, the only number that has the letter 'a' in it is 'one thousand'

÷

The division symbol '÷' is actually called an obelus

Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself

40 is spelt as forty and not 'fourty'. It is the only number that is spelt with letters arranged in alphabetical order

An odd number is a number that cannot be divisible by 2.

Every odd number has an 'e' in its spelling. They include:

  • One
  • Three
  • Five
  • Seven
  • Nine

555 in Thailand sounds like 'hahaha'. This is because the number '5' means 'ha' in Thailand

In mathematics, 10! means 10 factorial. Below is its calculation:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

Interestingly, 3628800 seconds is the same as 42 days

42 days is the same as 6 weeks

We can therefore say that 10! equals 6 weeks or 3628800 seconds in mathematics

When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321


Notable points in Mathematics

Let's use algebra to explain the simple statement below:

I am a number. When you subtract 3 from me, the result is 9. what number am I ?

Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.

Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:

  • Let the number be y

  • y - 3 = 9

  • y = 9 + 3

  • y = 12

Please read more on algebra here

Sides of a right angle triangle - Len Academy

 

The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ. Below are some points to note:

Hypotenuse is always the longest side of the triangle.

Opposite is the side opposite the angle (θ)

Adjacent is the shorter side next to the angle (θ)

Each of Sin θ, cos θ and tan θ are the ratio of sides of the right triangle. They are calculated by using the formula (margic word) sohcahtoa:

Sohcahtoa - Len Academy

soh

Sin θ = Opposite/Hypotenuse

cah

Cos θ = Adjacent/Hypotenuse

toa

Tan θ = Opposite/Adjacent

Please read more on sine, cosine and tangent here

Circumference of a Circle - Len Academy

Circumference in mathematics means the distance around the edge of a circle (or a another curved surface).

Circumference is to circle or any other curved surface

Perimeter of a Rectangle - Len Academy

Perimeter means the distance around a square or rectangle or polygon.

Perimeter is to square or rectangle or polygon