Binary number of number system in information communication technology lecture-.ppt

Binary number

1. Binary Number System
And Conversion
Digital Electronics

2. Bridging the Digital Divide
721
234
5
3
4
6
3
93523
1
3
7
275
16
9
3
5
145
00100
0101011
1
0
1
0
1
0
1
0
10010
1101
0
1
1
0
1
1
1101
010
0
0
1
0
1
1
0
1
00100
0101011
0
1
1
0
1
1
1101
0
0
1
0
1
1
0
1
00100
001011
1
0
1
0
1
0
1
0
10010
1101
0
1
1
0
1
1
1101
010
0
0
1
0
1
1
0
1
00100
0
1
0
1
0
1
1
011011
1101
0
0
1
0
1
10010 10010
00101101
721
234
53463 935
2
3
137275
1
6
935
145
Binary-to-Decimal
Conversion
Decimal-to-Binary
Conversion
2

3. Decimal to Binary Conversion
‒ ‒
The Process : Successive Division
a)Divide the Decimal Number by 2; the remainder is the LSB of
Binary Number .
b)If the quotation is zero, the conversion is complete; else repeat
step (a) using the quotation as the Decimal Number. The new
remainder is the next most significant bit of the Binary Number.
Example:
Convert the decimal number 6
10
into its binary equivalent.
Bit tSignifican Most 1 r
0
1 2
1 r
1
3 2
Bit tSignifican Least 0 r
3
6 2



 6
10
= 110
2
3

4. Dec → Binary : Example #1
Example:
Convert the decimal number 26
10 into its binary equivalent.
4

5. Dec → Binary : Example #1
Example:
Convert the decimal number 26
10 into its binary equivalent.
Solution:
LSB 0 r
13
26 2 
MSB 1 r
0
1 2 
1 r
6
13 2 
0 r
3
6 2 
1 r
1
3 2 
 26
10
= 11010
2
5

6. Dec → Binary : Example #2
Example:
Convert the decimal number 41
10 into its binary equivalent.
6

7. Dec → Binary : Example #2
Example:
Convert the decimal number 41
10 into its binary equivalent.
Solution:
LSB 1 r
20
41 2 
0 r
10
20 2 
0 r
5
10 2 
1 r
2
5 2 
 41
10
= 101001
2
MSB 1 r
0
1 2 
0 r
1
2 2 
7

8. Dec → Binary : More Examples
a)13
10
= ?
b)22
10 = ?
c)43
10 = ?
d)158
10 = ?
8

9. Dec → Binary : More Examples
a)13
10
= ?
b)22
10 = ?
c)43
10 = ?
d)158
10 = ?
1 1 0 1
2
1 0 1 1 0
2
1 0 1 0 1 1
2
1 0 0 1 1 1 1 0
2
9

10. Binary to Decimal Process
‒ ‒
The Process : Weighted Multiplication
a)Multiply each bit of the Binary Number by it corresponding bit-
weighting factor (i.e. Bit-0→2
0
=1; Bit-1→2
1
=2; Bit-2→2
2
=4; etc).
b)Sum up all the products in step (a) to get the Decimal Number.
Example:
Convert the binary number 0110
2 into its decimal equivalent.
 0110
2 = 6
10
0110
2
3
2
2
2
1
2
0
8 4 2 1
0+4+2+0=6
10
Bit-Weighting
Factors
10

11. Binary → Dec : Example #1
Example:
Convert the binary number 10010
2 into its decimal equivalent.
11

12. Binary → Dec : Example #1
Example:
Convert the binary number 10010
2 into its decimal equivalent.
10010
2 = 18
10
10010
2
4
2
3
2
2
2
1
2
0
16 8 4 2 1
16+0+0+2+0=18
10
Solution:
12

13. Binary → Dec : Example #2
Example:
Convert the binary number 0110101
2 into its decimal
equivalent.
13

14. Binary → Dec : Example #2
Example:
Convert the binary number 0110101
2 into its decimal
equivalent.
0110101
2 = 53
10
0110101
2
6
2
5
2
4
2
3
2
2
2
1
2
0
64 32 16 8 4 2 1
0+32+16+0+4+0+1=53
10
Solution:
14

15. Binary → Dec : More Examples
a)0110
2
= ?
b)11010
2 = ?
c)0110101
2 = ?
d)11010011
2 = ?
15

16. Binary → Dec : More Examples
a)0110
2
= ?
b)11010
2 = ?
c)0110101
2 = ?
d)11010011
2 = ?
6
10
26
10
53
10
211
10
16

17. Summary & Review
Successive
Division
a)Divide the Decimal Number by 2; the remainder is the LSB of Binary
Number .
b)If the Quotient Zero, the conversion is complete; else repeat step (a) using
the Quotient as the Decimal Number. The new remainder is the next most
significant bit of the Binary Number.
a)Multiply each bit of the Binary Number by it corresponding bit-weighting
factor (i.e. Bit-0→2
0
=1; Bit-1→2
1
=2; Bit-2→2
2
=4; etc).
b)Sum up all the products in step (a) to get the Decimal Number.
Weighted
Multiplication
17

18. Image Resources
•Microsoft, Inc. (2008). Clip Art. Retrieved March 15, 2008 from
http://office.microsoft.com/en-us/clipart/default.aspx
18