This document discusses binary numbers and how they are used in computers. It begins by explaining that binary is the primary language of computers, representing numbers with patterns of 1s and 0s. It then covers how to convert decimal numbers to binary using repeated division by 2. Each decimal place value is represented by a binary digit. The document also discusses how computers interpret bits and bytes to represent information. Overall, it provides an introduction to binary number systems and how they are used in digital computing.

1. TLE
Computer
Decimal - Binary
PERFORMING MENSURATION AND
CALCULATION (PMC)
9TH GRADE

2. Binary is the primary language of computer and a
system of representing numbers using a pattern of
ones and zeroes.
First invented by Gottfried Leibniz in the 17th
century,
the binary number system became widely used
once
computers required a way to represent numbers
using mechanical switches
What Is Binary and How Does It
Work?

3. Decimal - Binary
While human interpret words and
pictures, Computers interpret only
patterns of bits.
bits - short for binary digit either 0 or 1
Byte – a unit of computer information consisting of eight (8)
bits
1 byte is equal to 8 bits
1byte=8bits

4. Decimal - Binary
While human interpret words and
pictures, Computers interpret only
patterns of bits.
bits - short for binary digit either 0 or 1
Byte – a unit of computer information consisting of eight (8)
bits
1 byte is equal to 8 bits
1byte=8bits

5. Decimal – Binary
1st Method
To convert a decimal number to
binary, all you have to do is
divide the number by 2. Get the
quotient and the remainder.
Bring down the quotient, divide
it by 2, and get the quotient and
remainder again. Do it
repeatedly until the quotient
results to 0. Copy the
remainder from bottom to top,
and that is the binary
equivalent
EX: 3010
Quotient Remainder
30 / 2
15 / 2
7 / 2
3 / 2
1 / 2
15
7
3
1
0
0
1
1
1
1
3010 = 11110
3010 = 00011110 bytes

6. Decimal – Binary
1st Method
To convert a decimal number to
binary, all you have to do is
divide the number by 2. Get the
quotient and the remainder.
Bring down the quotient, divide
it by 2, and get the quotient and
remainder again. Do it
repeatedly until the quotient
results to 0. Copy the
remainder from bottom to top,
and that is the binary
equivalent
EX: 2010
?
Quotient
?
Remainder
?

7. Decimal – Binary
1st Method
To convert a decimal number to
binary, all you have to do is
divide the number by 2. Get the
quotient and the remainder.
Bring down the quotient, divide
it by 2, and get the quotient and
remainder again. Do it
repeatedly until the quotient
results to 0. Copy the
remainder from bottom to top,
and that is the binary
equivalent
EX: 20
Quotient Remainder
20 / 2
10 / 2
5 / 2
2/ 2
1 / 2
10
5
2
1
0
0
0
1
0
1
20 = 10100
20 = 00010100 bytes

8. Decimal – Binary
2nd Method
EX: 3010
3010 = 11110
3010 = 00011110 bytes

9. Decimal – Binary
2nd Method
EX: 2010
2010 = 10100
2010 = 00010100 bytes

10. Binary – Decimal
2nd Method
What is the Decimal Value of
00010100 bytes = ?

11. Binary – Decimal
2nd Method
What is the Decimal Value of
00010100 bytes = 2010

12. Binary – Decimal
2nd Method
What is the Decimal Value of
01000001 bytes = ?

13. Binary – Decimal
2nd Method
What is the Decimal Value of
01000001 bytes = 6510

14. UPPERCASE
Binary Text Conversion

15. Binary Text Conversion
LOWERCASE

16. Binary Text Conversion

17. What are the Binary Code
for the word TLE?
Binary Text Conversion

18. What are the Binary Code
for the word TLE?
T=01010100
L=01001100
E=01000101
Binary Text Conversion

19. What are the Decimal Numbe
represented for the word TLE
T=01010100
L=01001100
E=01000101
Binary Text Conversion

20. What are the Decimal Numbe
represented for the word TLE
T=01010100 =84
L=01001100 =76
E=01000101 =69
Binary Text Conversion

21. SHORT QUIZ
1. How do we represent 15 in Binary
form?
2. How do we represent 32 in Binary
form?
3. How do we represent 09 in Binary
form?
4. How do we represent 254 in Binary
form?
5. What Decimal number is
represented by the binary number
00000011?

22. Binary Text Conversion
What are the Decimal
Number
represented for the
number 2023?

23. Binary Text Conversion
What are the Decimal
Number
represented for the
number 2023?
2=50
0=48
2=50
3=53