Mathematics (VIII)

Abdullah Al Mahmud

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Binary Numbers

Chapter Info

Total Session: 10

Concept of Binary Numbers
Characteristics of Binary Numbers
Conversion
Binary Addition
Complement
Subtraction
Multiplication

Session 01 (Concept)

History of Binary

Wilhelm Leibniz
Explanation of the Binary Arithmetic (1703)
Decimal to Binary

George Boole
The Mathematical Analysis of Logic (1847)
Real Life with 0 & 1 (Truth & False)

Quiz

10 Minutes

Groups of 4

What is the full form of Bit?
Why does the binary system use two digits only? Explain.
Express the binary number 1011 in decimal form.
What will be the number if we express 11 from Binary to Decimal?

Think

What is the use of Binary Numbers?

Session 02 (Characteristics)

Recap

What is the use of Binary Numbers?

Number Base

Decimal: \((134)_{10}\)
Binary: \((1101)_2\)

Number Using 01

Decimal	0	1	2	3	4	5	6	7
Decimal	1	1	10

Place Value

Write place value of each digit of the Binary number \((11011)_2\)

Radix

Significant Digit

Decimal: \((134)_{10}\)
Binary: \((1101)_2\)

MSB and LSB

Digital machine

Can Detect 0 and 1

Digital Clock
Digital Scale

Group Work

2 Groups

Question and Answers

Example

1. What is Base?
1. Find place value of 15644 & 1111
1. Integer, Radix, and Fraction: 154.876
1. Full Meaning of Bit
1. LSB, MSB: 198, 1011
1. Why o, 1 in Digital Machine

Session 03 (Conversion)

Fraction

Convert 23.25 to binary

Integer: Divide \(\rightarrow\) \(MSB \to LSB\)

Fraction: Multiply \(\to LSB \to MSB\)

Multiplication	Integer	Decimal
0.8125 x 2	1	0.625
0.625 x 2	1	0.250
0.250 x 2	0	0.50
0.50 x 2	1	-

D-B Alternative

14 \(\to\)

Binary to Decimal

B-D Alternative

1	2	4	8	16	32	64
0	1	0	1	0	1	0

What number do we have?

Make Number

Make a binary number of your choice

Individual task

1	2	4	8	16	32	64
-	-	-	-	-	-	-

Decimal to Binary (Fraction)

Keep multiplying fractional part by 2 until the product is 1.0

Binary to Decimal (Fraction)

Conversion Tasks

\((976)_{10}\)
Your CADET NO.