Binary Placement Chart

Binary Placement Chart

2 10

2

2

1024

512

256

2

2

2 2 2 3 2 2 2 1 2

128 64 32 16 8 4 2 1

Octal Placement Chart

8

8

8

8

8 3

8 2

8 1

8

2097152 262144 32768 4096 512

64

8

1

Hexadecimal Placement Chart

16

16

16 3

16 2

16 1

16

1048576 65536 4096 256

16

1

Steps to convert Decimal-to-Binary 1. Find the highest value that is your number. 2. Turn the switch on. (Mark a 1) 3. Subtract the value from your number. 4. If the remainder is zero, turn all other switches off. (Mark a 0) 5. If the remainder is NOT zero, then repeat steps 1-4. Example

2 10

2

1024

512

49 - 32

17 - 16

1 - 1

0 stop

2

2

2

256

128 64

Answer: 4910= 1100012

2 2 2 3 2 2 2 1 2 32 16 8 4 2 1 1 1 0 0 01

Steps to convert Binary-to-Decimal 1. Starting from right to left, plug your numbers into the placement chart. 2. Add all values where the switch is on. (Where there is a 1) Example

2 10

2

2

1024

512

256

32 + 16 + 1 = 49 Answer: 1100012 = 4910

2

2

2 2 2 3 2 2 2 1 2

128 64 32 16 8 4 2 1 1 1 0 0 01

Steps to convert Binary-to-Octal 1. Break the binary number into 3-bit sections (starting from right to left). If there are digits left over,

add additional zeroes in order to create a 3 digit group. 2. Then, determine what octal number (0-7) each 3-digit code represents. Example 100101010 100 | 101 | 010

2 2 2 1 2 4 2 1 10 0

=

4

2 2 2 1 2 4 2 1 10 1

=

5

2 2 2 1 2 4 2 1 01 0

=

2

Answer: 1001010102 = 4528

Steps to convert Octal-to-Binary Determine the 3-digit group (binary number) that corresponds to each octal number.

6

=

2 2 2 1 2 4 2 1 1 10

0

=

2 2 2 1 2 4 2 1 0 0 0

3

=

Answer: 6038 = 1100000112

2 2 2 1 2 4 2 1 0 11

Steps to convert Octal-to-Decimal 1. Starting from right to left, plug your numbers into the placement chart. 2. Multiply each octal number by the value above it. 3. Add all those values up.

8

8

8

8

8 3

8 2

8 1

8

2097152 262144 32768 4096 512

64

8

1

6

0

3

(64*6) + (8*0) + (1*3) = 384 + 0 + 3 = 387

Answer: 6038 = 38710

Steps to convert Hexadecimal-to-Binary Find the 4-digit group that corresponds to each hexadecimal number.

Decimal

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F

Binary

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

7

=

0111

5

=

0101

C

=

1100

E

=

1110

Answer: 75CE16 = 01110101110011102 = 1110101110011102

(NOTE: You can leave off any leading zeroes.)

Steps to convert Binary-to-Hexadecimal

1. Break the binary number into 4-bit sections (starting from right to left). If there are digits left over, add additional zeroes in order to create a 4-digit group.

2. Then, determine what hexadecimal number (0-F) each 4-digit code represents.

100101010 0001 | 0010 | 1010

1 2 A

Answer: 1001010102 = 0001001010102 = 12A16

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