Number System Conversion from binary to decimal ,decimal to binary & etc

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Number system Conversion

Course Contents
• Number System, BCD and Parity bit, Boolean Algebra, Basic and Universal
Logic Gates, Standard forms, Boolean expression simplification using Karnaugh
map, even considering "don't care" condition, Adder, Subtractor, Decoder,
Encoder and priority Encoder, Multiplexer, De-multiplexer, Latch and Flipflop,
Counters and Shift Registers, static random-access memory (SRAM), and ROM,
Programmable Logic Devices (PROM, PAL, PLA).
Description:
Digital Electronics course provides an introduction to the control of engineering
systems using programmable logic, with specific focus on programmable logic
devices. The course rational is define form the context of digital logic, digital
arithmetic, programmable logic and computer architecture. Design simple
combinational logics using basic gates and to optimize Boolean logic using
Karnaugh map, even considering "don't care" condition. The course will also
introduce the basic sequential logic components.
2

Ref. Books:
Textbook/Recommended Readings:
•Digital Logic Design – Morris Mano (5th Edition)
•Digital Fundamentals- Floyd (8th Edition)
Reference Books/Supplementary Readings:
•Digital Systems-Principles and Application- Tocci (10th
Edition)
3

What is Digital Systems?
Digital systems are described as systems that use discrete
signals to represent and process information.
4
4
3
2
3
1 1 1
4
3.7
3.1
2.2

Number Systems
• Base = 2  Binary (0,1)
• Base = 8  Octal (0-7)
• Base = 10  Decimal (0-9)
• Base = 16  Hexadecimal (0-9,A-F)
(A=10, B=11, C=12, D=13, E=14, F=15)
6

Base-n to Decimal Conversion
(abc.de)n = (a*n2
+ b*n1
+ c*n0
+ d*n-1
+ e*n-2
)10
8
(315.42)6 = (3*62
+ 1*61
+ 5*60
+ 4*6-1
+ 2*6-2
)10
n = Base number

9
Converting binary numbers to
decimal
• What is 10011010 in decimal?
10011010 = 1*27
+ 0*26
+ 0*25
+ 1*24
+ 1*23
+
0*22
+ 1*21
+ 0*20
= 27
+ 24
+ 23
+ 21
= 128 + 16 + 8 + 2
= 154
• What is 00101001 in decimal?
00101001 = 0*27
+ 0*26
+ 1*25
+ 0*24
+ 1*23
+
0*22
+ 0*21
+ 1*20
= 25
+ 23
+ 20
= 32 + 8 + 1
= 41

10
Converting binary numbers to
decimal
• What is 10011010.1101 in decimal?
10011010 .1101 = 1*27
+ 0*26
+ 0*25
+ 1*24
+ 1*23
+
0*22
+ 1*21
+ 0*20
+ 1*2-1
+ 1*2-2
+ 0*2-3
+
1*2-4
= 27
+ 24
+ 23
+ 21
+ 2-1
+ 2-2
+ 2-4
= 128 + 16 + 8 + 2 + .5 + .25 + 0.0625
= 154.8125
• What is 00101001.0001 in decimal?
00101001.0001 = 25
+ 23
+ 20
+ 2-4
= 32 + 8 + 1 + 0.0625
= 41.0625

Octal & Hexadecimal numbers
to Decimal
• (F1)16 = 15*161
+ 1*160
= (241)10
• (62)8 = 6*81
+ 2*80
= (50)10
11

Decimal to Base-n conversion
Step-by-step:
•Divide the decimal number by the base
number (n)
•Find out the quotient and remainder
•Divide the quotient by the base number (n)
again and keep the remainders in a serial
•Continue this process until you find quotient =
0
•MSB = last remainder, LSB = first remainder
12

13
Decimal numbers to binary
Most Significant Bit (MSB)
Least Significant Bit (LSB)

$Decimal Fraction to Base-n conversion Step-by-step: •Multiply the fraction by the base number (n) •Find out the product and carry, do (product - carry) •Multiply the number by the base number (n) again and keep the carry in a serial •Continue this process until you find product = 0 (not always necessary) •MSB = first carry, LSB = last carry 14$

16
Decimal Numbers to Binary
• 53 = 32 + 16 + 4 + 1
= 25
+ 24
+ 22
+ 20
= 1*25
+ 1*24
+ 0*23
+ 1*22
+ 0*21
+ 1*20
= 110101 in binary
= 00110101 as a full byte in binary
• 211= 128 + 64 + 16 + 2 + 1
= 27
+ 26
+ 24
+ 21
+ 20
= 1*27
+ 1*26
+ 0*25
+ 1*24
+ 0*23
+ 0*22
+
1*21
+ 1*20
= 11010011 in binary

Octal and Hexadecimal to
Binary
Method 1:
•Octal/Hexadecimal to Decimal
•Decimal to Binary
Method 2: Direct Conversion
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Number System Conversion from binary to decimal ,decimal to binary & etc

1. CSE 223 : Digital Logic Design Lesson-01 Number System Conversions Md. Shadman Mostafa Dept. of CSE, Daffodil International University E-mail: shadmanrimo13@gmail.com 1

2. Course Contents • Number System, BCD and Parity bit, Boolean Algebra, Basic and Universal Logic Gates, Standard forms, Boolean expression simplification using Karnaugh map, even considering "don't care" condition, Adder, Subtractor, Decoder, Encoder and priority Encoder, Multiplexer, De-multiplexer, Latch and Flipflop, Counters and Shift Registers, static random-access memory (SRAM), and ROM, Programmable Logic Devices (PROM, PAL, PLA). Description: Digital Electronics course provides an introduction to the control of engineering systems using programmable logic, with specific focus on programmable logic devices. The course rational is define form the context of digital logic, digital arithmetic, programmable logic and computer architecture. Design simple combinational logics using basic gates and to optimize Boolean logic using Karnaugh map, even considering "don't care" condition. The course will also introduce the basic sequential logic components. 2

3. Ref. Books: Textbook/Recommended Readings: •Digital Logic Design – Morris Mano (5th Edition) •Digital Fundamentals- Floyd (8th Edition) Reference Books/Supplementary Readings: •Digital Systems-Principles and Application- Tocci (10th Edition) 3

4. What is Digital Systems? Digital systems are described as systems that use discrete signals to represent and process information. 4 4 3 2 3 1 1 1 4 3.7 3.1 2.2

5. 5 Digital Computer

6. Number Systems • Base = 2  Binary (0,1) • Base = 8  Octal (0-7) • Base = 10  Decimal (0-9) • Base = 16  Hexadecimal (0-9,A-F) (A=10, B=11, C=12, D=13, E=14, F=15) 6

7. 7

8. Base-n to Decimal Conversion (abc.de)n = (a*n2 + b*n1 + c*n0 + d*n-1 + e*n-2 )10 8 (315.42)6 = (3*62 + 1*61 + 5*60 + 4*6-1 + 2*6-2 )10 n = Base number

9. 9 Converting binary numbers to decimal • What is 10011010 in decimal? 10011010 = 1*27 + 0*26 + 0*25 + 1*24 + 1*23 + 0*22 + 1*21 + 0*20 = 27 + 24 + 23 + 21 = 128 + 16 + 8 + 2 = 154 • What is 00101001 in decimal? 00101001 = 0*27 + 0*26 + 1*25 + 0*24 + 1*23 + 0*22 + 0*21 + 1*20 = 25 + 23 + 20 = 32 + 8 + 1 = 41

10. 10 Converting binary numbers to decimal • What is 10011010.1101 in decimal? 10011010 .1101 = 1*27 + 0*26 + 0*25 + 1*24 + 1*23 + 0*22 + 1*21 + 0*20 + 1*2-1 + 1*2-2 + 0*2-3 + 1*2-4 = 27 + 24 + 23 + 21 + 2-1 + 2-2 + 2-4 = 128 + 16 + 8 + 2 + .5 + .25 + 0.0625 = 154.8125 • What is 00101001.0001 in decimal? 00101001.0001 = 25 + 23 + 20 + 2-4 = 32 + 8 + 1 + 0.0625 = 41.0625

11. Octal & Hexadecimal numbers to Decimal • (F1)16 = 15*161 + 1*160 = (241)10 • (62)8 = 6*81 + 2*80 = (50)10 11

12. Decimal to Base-n conversion Step-by-step: •Divide the decimal number by the base number (n) •Find out the quotient and remainder •Divide the quotient by the base number (n) again and keep the remainders in a serial •Continue this process until you find quotient = 0 •MSB = last remainder, LSB = first remainder 12

13. 13 Decimal numbers to binary Most Significant Bit (MSB) Least Significant Bit (LSB)

14. Decimal Fraction to Base-n conversion Step-by-step: •Multiply the fraction by the base number (n) •Find out the product and carry, do (product - carry) •Multiply the number by the base number (n) again and keep the carry in a serial •Continue this process until you find product = 0 (not always necessary) •MSB = first carry, LSB = last carry 14

15. Decimal Fraction to Binary 15

16. 16 Decimal Numbers to Binary • 53 = 32 + 16 + 4 + 1 = 25 + 24 + 22 + 20 = 1*25 + 1*24 + 0*23 + 1*22 + 0*21 + 1*20 = 110101 in binary = 00110101 as a full byte in binary • 211= 128 + 64 + 16 + 2 + 1 = 27 + 26 + 24 + 21 + 20 = 1*27 + 1*26 + 0*25 + 1*24 + 0*23 + 0*22 + 1*21 + 1*20 = 11010011 in binary

17. Octal and Hexadecimal to Binary Method 1: •Octal/Hexadecimal to Decimal •Decimal to Binary Method 2: Direct Conversion 17

18. Binary to Octal and Hexadecimal 18

19. 19 Hexadecimal to Octal

20. 20 THANK YOU

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