The document discusses binary number conversion between decimal and binary representations. It provides two processes: 1) Decimal to binary conversion uses successive division, where the decimal number is divided by 2 and the remainders form the binary number bits. 2) Binary to decimal conversion uses weighted multiplication, where each bit of the binary number is multiplied by its place value and the products are summed to obtain the decimal number. Worked examples demonstrate converting specific values between decimal and binary.

1. Binary Number System
And Conversion

2. Bridging the Digital Divide
16 2 3
3
64 721 93355 3 16 63
2
Decimal-to-Binary
3 721 53
935 Conversion
5 5 4
234 1257137 2
9 935
13 75
4 34
7 145 2
01 01 0010
01 01
10011 1 100010110 01 0
0
010 1101 010 1 1 01011
01 1
1100
001 0
10
11 0
001
011 00 010 01 0 1
01
01 101
1 1 011011
01 110 001010010
Binary-to-Decimal
Conversion 101 101 0
1 11 01
01010 11 0 0101011
1001
0
0 1 01
101
1001
011101
1 0 00 1 001011
00
1 1 00 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 610 into its binary equivalent.
3
2 6 r = 0 ← Least Significant Bit
1
2 3 r =1 ∴ 610 = 1102
0
2 1 r = 1 ← Most Significant Bit
3

4. Dec → Binary : Example #1
Example:
Convert the decimal number 2610 into its binary equivalent.
4

5. Dec → Binary : Example #1
Example:
Convert the decimal number 2610 into its binary equivalent.
Solution:
13
2 26 r = 0 ← LSB
6
2 13 r =1
3
2 6 r=0 ∴ 2610 = 110102
1
2 3 r =1
0
2 1 r = 1 ← MSB
5

6. Dec → Binary : Example #2
Example:
Convert the decimal number 4110 into its binary equivalent.
6

7. Dec → Binary : Example #2
Example:
Convert the decimal number 4110 into its binary equivalent.
Solution:
20
2 41 r = 1 ← LSB
10
2 20 r=0
5
2 10 r=0 ∴ 4110 = 1010012
2
2 5 r =1
1
2 2 r=0
0
2 1 r = 1 ← MSB 7

8. Dec → Binary : More Examples
a) 1310 = ?
b) 2210 = ?
c) 4310 = ?
d) 15810 = ?
8

9. Dec → Binary : More Examples
a) 1310 = ? 11012
b) 2210 = ? 101102
c) 4310 = ? 1010112
d) 15810 = ? 100111102
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→20=1; Bit-1→21=2; Bit-2→22=4; etc).
b) Sum up all the products in step (a) to get the Decimal Number.
Example:
Convert the decimal number 01102 into its decimal equivalent.
0 1 1 0
23 22 21 20
Bit-Weighting ∴ 0110 2 = 6 10
8 4 2 1 Factors
0 + 4 + 2 + 0 = 610
10

11. Binary → Dec : Example #1
Example:
Convert the binary number 100102 into its decimal equivalent.
11

12. Binary → Dec : Example #1
Example:
Convert the binary number 100102 into its decimal equivalent.
Solution:
1 0 0 1 0
24 23 22 21 20
16 8 4 2 1
16 + 0 + 0 + 2 + 0 = 1810
∴100102 = 1810
12

13. Binary → Dec : Example #2
Example:
Convert the binary number 01101012 into its decimal
equivalent.
13

14. Binary → Dec : Example #2
Example:
Convert the binary number 01101012 into its decimal
equivalent.
Solution:
0 1 1 0 1 0 1
26 25 24 23 22 21 20
64 32 16 8 4 2 1
0 + 32 + 16 + 0 + 4 + 0 + 1 = 5310
∴01101012 = 5310
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 = ? 6 10
b) 11010 2 = ? 26 10
c) 0110101 2 = ? 53 10
d) 11010011 2 = ? 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.
Weighted
Multiplication
a) Multiply each bit of the Binary Number by it corresponding bit-weighting
factor (i.e. Bit-0→20=1; Bit-1→21=2; Bit-2→22=4; etc).
b) Sum up all the products in step (a) to get the Decimal Number.
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