binary01.ppt decimal decimal: base 10 means 10 unique numerical digits 0 1 2 3 4 5 6 7 8 9 1 1 1 1 1...

Binary01.ppt

DecimalDecimal: Base 10 means 10 Unique numerical digits

0 1 2 3 4 5 6 7 8 9

1 1 1 1 1

1101001,00010,000Weight Positions

3, 4 6 710

3 x 1000 = 3000

4 x 100 = 400

6 x 10 = 60

7 x 1 = 7

------------------------

3,467

etc.

Binary01.ppt

DecimalAddition

0 1 2 3 4 5 6 7 8 9

3

+ 5--------- 8 start +1 +2 +3 +4 +5

6

+ 7--------- 13

0 1 2 3 4 5 6 7 8 9

start +1 +2 +3+6 +7+4 +5

Carry 1

Binary01.ppt

BinaryDecimal: Base 2 means 2 Unique numerical digits

0 1 On Off In Out Left Right

1 1 1 1 1 1

12 4 816Decimal Weight Positions

32etc.

1 0 1 1 0 12

1 x 32 = 32

0 x 16 = 0

1 x 8 = 8

1 x 4 = 4

0 x 2 = 0

1 x 1 = 1

------------------------

4510

Binary01.ppt

BinaryAddition

0+ 0------ 0

1+ 0------ 1

0+ 1------ 1

1

1 + 1 ------ 1 0with a 1 carry

1 0 1 1 0 1 0 1 1

0 0 1 0 0 1 0 0 1

1 1 0 1 1 0 1 0 0

1 1 1 1 Carry

Binary01.ppt

HexadecimalDecimal: Base 16 means 16 Unique numerical digits

0 1 2 3 4 5 6 7 8 9

A B C D E F

Decimal Equivalents

0 = 0

1 = 1

2 = 2

3 = 3

4 = 4

5 = 5

6 = 6

7 = 7

8 = 8

9 = 9

A = 10

B = 11

C = 12

D = 13

E = 14

F = 15

Binary01.ppt

Hexadecimal

0-F 0-F 0-F 0-F 0-F 0-F

1,048,576 65,536 4,096 256 16 1

Decimal Weight Positions

A 3 9 D 6 C16

A = 10 X 1,048,576 = 10,485,760

+ 3 = 3 X 65,536 = 196,608

+ 9 = 9 X 4096 = 36,864

+ D = 13 X 256 = 3,328

+ 6 = 6 X 16 = 96

+ C = 12 X 1 = 12

------------------------------------------------------

10,722,66810

Binary01.ppt

Hexadecimalto Binary

0 = 0000

1 = 0001

2 = 0010

3 = 0011

4 = 0100

5 = 0101

6 = 0110

7 = 0111

8 = 1000

9 = 1001

A = 1010

B = 1011

C = 1100

D = 1101

E = 1110

F = 1111

It takes 4 bits to make one Hex number

Binary01.ppt

Octal

Decimal: Base 8 means 8 Unique numerical digits

0 1 2 3 4 5 6 7

Decimal Equivalents

0 = 0

1 = 1

2 = 2

3 = 3

4 = 4

5 = 5

6 = 6

7 = 7

Octal to Binary

0 = 000

1 = 001

2 = 010

3 = 011

4 = 100

5 = 101

6 = 110

7 = 111

It takes 3 bits to make one Octal number

Binary01.ppt

1 1 1 1

1864512

Decimal Weight Positions

Octal

7 5 2 38

7 x 512 = 3,584

16 x 5 = 80

2 x 8 = 16

3 x 1 = 3

-------

3,68310

Binary01.ppt

Binary to Decimal

1 0 1 1 0 1 0 1

Decimal Weights128 32 16 4 1 = 18110

Add the decimal weights of the “1” bits

Decimal to Binary1. Find the largest binary bit that will fit in the number without going over the number

2. Mark that bit as “on” and subtract the bit weight value from the decimal number

3. Repeat steps 1 and 2 until there are no more numbers remaining in the decimal number

Binary01.ppt

Hex to Binary

C 5 9 B16

1100 0101 1001 10112 11000101100110112=

Convert Hex to Binary

Binary to HexDivide bits into groups of 4

11000101100110112

C 5 9 B16

1.

2.

3.

1100 0101 1001 10112

Binary01.ppt

Binary to OctalDivide bits into groups of 3

11000101100110112

1 4 2 6 3 38

1.

2.

3.

1 100 010 110 011 0112

Octal to Binary1 4 2 6 3 38

001 100 010 110 011 0112

Binary01.ppt

Hex to Octal to DecimalBreak the hex or octal or decimal number into binary

1 0 1 1 1 0 0 0 1 0 1 1

2048 512 256 128 8 2 1

Decimal: add the weights = 2,95510

Hexadecimal: divide the bits into patterns of 4 = B8B16

Octal: divide the bits into patterns of 3 = 56138