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Binary Number System And Conversion

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Page 1: Binary numbersystem1

Binary Number System And Conversion

Page 2: Binary numbersystem1

Bridging the Digital Divide

721234534

6393523

137275

16

935

145

00100

0101011

1010

1010100101 1 0

1

0110111101

010

00101101

00100

0101011

011011

1101

00101101

00100

0010111010

1

010100101 1 0

1

0110111101

010

00101101

00100

0101011

011011

110100101

10010 10010

00101101

721234

53463 935

23

137275

16

935

145

Binary-to-DecimalConversion

Decimal-to-BinaryConversion

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Page 3: Binary numbersystem1

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.

Bit tSignifican Most 1 r 0 1 2

1 r 1 3 2

Bit tSignifican Least 0 r 3 6 2

←=

=

←=

∴ 610 = 1102

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Page 4: Binary numbersystem1

Dec → Binary : Example #1Example:

Convert the decimal number 2610 into its binary equivalent.

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Page 5: Binary numbersystem1

Dec → Binary : Example #1Example:

Convert the decimal number 2610 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 =

∴ 2610 = 110102

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Page 6: Binary numbersystem1

Dec → Binary : Example #2Example:

Convert the decimal number 4110 into its binary equivalent.

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Page 7: Binary numbersystem1

Dec → Binary : Example #2Example:

Convert the decimal number 4110 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 =

∴ 4110 = 1010012

MSB 1 r 0 1 2 ←=

0 r 1 2 2 =

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Page 8: Binary numbersystem1

Dec → Binary : More Examples

a) 1310 = ?

b) 2210 = ?

c) 4310 = ?

d) 15810 = ?

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Page 9: Binary numbersystem1

Dec → Binary : More Examples

a) 1310 = ?

b) 2210 = ?

c) 4310 = ?

d) 15810 = ?

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

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Page 10: Binary numbersystem1

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.

∴ 0110 2 = 6 10

0 1 1 023 22 21 20

8 4 2 1

0 + 4 + 2 + 0 = 610

Bit-Weighting Factors

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Page 11: Binary numbersystem1

Binary → Dec : Example #1Example:

Convert the binary number 100102 into its decimal equivalent.

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Page 12: Binary numbersystem1

Binary → Dec : Example #1Example:

Convert the binary number 100102 into its decimal equivalent.

∴100102 = 1810

1 0 0 1 024 23 22 21 20

16 8 4 2 1

16 + 0 + 0 + 2 + 0 = 1810

Solution:

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Page 13: Binary numbersystem1

Binary → Dec : Example #2Example:

Convert the binary number 01101012 into its decimal equivalent.

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Page 14: Binary numbersystem1

Binary → Dec : Example #2Example:

Convert the binary number 01101012 into its decimal equivalent.

∴01101012 = 5310

0 1 1 0 1 0 126 25 24 23 22 21 20

64 32 16 8 4 2 1

0 + 32 + 16 + 0 + 4 + 0 + 1 = 5310

Solution:

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Page 15: Binary numbersystem1

Binary → Dec : More Examples

a) 0110 2 = ?

b) 11010 2 = ?

c) 0110101 2 = ?

d) 11010011 2 = ?

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Page 16: Binary numbersystem1

Binary → Dec : More Examples

a) 0110 2 = ?

b) 11010 2 = ?

c) 0110101 2 = ?

d) 11010011 2 = ?

6 10

26 10

53 10

211 10

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Page 17: Binary numbersystem1

Summary & Review

SuccessiveDivision

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→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.

WeightedMultiplication

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