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Posted on Jan 02, 2017

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Decimal is base 10 and binary is base 2.

The columns from right to left in base 10 are:

10^10 10^9 10^8 10^7 10^6 10^5 10^4 10^3 10^2 10^1 10^0

Similarly, the columns from right to left in base 2 are:

2^10 2^9 2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

This site does a good job of explaining the conversion from decimal to binary.

http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary

For example, take the number 157. The biggest column that goes into 157 is 128, which is the 2^7th column, so we put 1 in that column. Subtracting 128 from157, we get 29. We start all over again. The biggest binary number going into 29 is 16, which is the 2^4th column. When you subtract 16 from 29, you get 13. We start all over again. The biggest binary number going into 13 is 8. Subtracting 8 from 13, we get 5. Biggest number going in is 4, 2^2th column. 1 left over to go into the 2^0 column.

Pulling it all together, we get:

10011101.

Checking, 128 + 16 + 8 + 4 + 1 = 157.

Good luck.

Let me know if you have any questions.

Paul

The columns from right to left in base 10 are:

10^10 10^9 10^8 10^7 10^6 10^5 10^4 10^3 10^2 10^1 10^0

Similarly, the columns from right to left in base 2 are:

2^10 2^9 2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

This site does a good job of explaining the conversion from decimal to binary.

http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary

For example, take the number 157. The biggest column that goes into 157 is 128, which is the 2^7th column, so we put 1 in that column. Subtracting 128 from157, we get 29. We start all over again. The biggest binary number going into 29 is 16, which is the 2^4th column. When you subtract 16 from 29, you get 13. We start all over again. The biggest binary number going into 13 is 8. Subtracting 8 from 13, we get 5. Biggest number going in is 4, 2^2th column. 1 left over to go into the 2^0 column.

Pulling it all together, we get:

10011101.

Checking, 128 + 16 + 8 + 4 + 1 = 157.

Good luck.

Let me know if you have any questions.

Paul

May 14, 2016 | Office Equipment & Supplies

Let's do the preocess so it will work on any calculator.

As an example, convert 68 from decimal to binary.

The decimal columns are 10^0, 10^1, 10^2, 10^3, etc.

The binary columns are 2^0, 2^1, 2^2, 2^3, etc.

Flipping to the normal left to right, we get 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0.

64 32 16 8 4 2 1

We divide our number, 68, by 64, and get 1 with a remainder of 4. We next divide our remainder by 32, 16, 8, and finally 4, where we get 1 with no reminder.

In binary, this works out to 1000100. To check, we multiply the ones by the respective column values and get 64 + 4 = 68.

Good luck.

Paul

As an example, convert 68 from decimal to binary.

The decimal columns are 10^0, 10^1, 10^2, 10^3, etc.

The binary columns are 2^0, 2^1, 2^2, 2^3, etc.

Flipping to the normal left to right, we get 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0.

64 32 16 8 4 2 1

We divide our number, 68, by 64, and get 1 with a remainder of 4. We next divide our remainder by 32, 16, 8, and finally 4, where we get 1 with no reminder.

In binary, this works out to 1000100. To check, we multiply the ones by the respective column values and get 64 + 4 = 68.

Good luck.

Paul

Feb 28, 2016 | Casio FX-85GT Plus Scientific Calculator...

Where to start. Most things we do in math are in base 10, probably because we have 10 fingers. Instead of base 10, binary is base 2. In computers, binary rules because a bit can be set to ON or OFF, 1 being ON, and 0 being OFF.

So the next thing is counting. 0 1 10 11 100 101 110 111 1000 1001

Decimal equivalent 0 1 2 3 4 5 6 7 8 9

How to convert from binary to decimal? Line up the columns and multiply down. For example, 1101. The columns, starting from the right are 2^0, 2^1, 2^2, 2^3, reading ^ as exponent.

See if I can line these up. 1 1 0 1

2^3 2^2 2^1 2^0

8 4 2 1

multiplying down 8 4 0 1

Next step is to add them up. 8+4+1 = 13!

Going the other way, we have to divide by the largest 2^x number, so what is left over and continue dividing until nothing is left.

For example, 56. 2^5 (32) is the largest 2^x number that goes into 56, so we put a 1 in this column. Our remainder is 24. 2^4 (16) goes into this once, so we put a 1 in this column. Our remainder is 8. 2^3(8) goes into this once, so we put a 1 in this column. Now the remainder is 0 so we put a 0 in the 2^2 (4) column, 2^1(2) column, and 2^0 (1) column.

We end up with 111000.

Let me know if you have any questions.

Good luck.

Paul

So the next thing is counting. 0 1 10 11 100 101 110 111 1000 1001

Decimal equivalent 0 1 2 3 4 5 6 7 8 9

How to convert from binary to decimal? Line up the columns and multiply down. For example, 1101. The columns, starting from the right are 2^0, 2^1, 2^2, 2^3, reading ^ as exponent.

See if I can line these up. 1 1 0 1

2^3 2^2 2^1 2^0

8 4 2 1

multiplying down 8 4 0 1

Next step is to add them up. 8+4+1 = 13!

Going the other way, we have to divide by the largest 2^x number, so what is left over and continue dividing until nothing is left.

For example, 56. 2^5 (32) is the largest 2^x number that goes into 56, so we put a 1 in this column. Our remainder is 24. 2^4 (16) goes into this once, so we put a 1 in this column. Our remainder is 8. 2^3(8) goes into this once, so we put a 1 in this column. Now the remainder is 0 so we put a 0 in the 2^2 (4) column, 2^1(2) column, and 2^0 (1) column.

We end up with 111000.

Let me know if you have any questions.

Good luck.

Paul

Oct 26, 2015 | Office Equipment & Supplies

Supposedly easy to set, the conversion chart of traditional to binary time & the variety of information make this topic fit for a handoff to http://www.binarywatches.co.uk/binary-watch-information.html.

Dec 01, 2014 | Watches

To convert from binary to decimal, we have to line up the numbers with the binary columns.

1 1 1 0 0 0

2^5 2^4 2^3 2^2 2^1 2^0

32 16 8 4 2 1

32 + 16 + 8 + 0 + 0+ 0 = 56

Good luck.

Paul

1 1 1 0 0 0

2^5 2^4 2^3 2^2 2^1 2^0

32 16 8 4 2 1

32 + 16 + 8 + 0 + 0+ 0 = 56

Good luck.

Paul

Oct 03, 2014 | Office Equipment & Supplies

Let's start by setting up the binary columns.

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

Written horizontally.

128 64 32 16 8 4 2 1

1 1 1 1 1 1 1

What is the biggest number that goes into 127. 64. Put 1 in the 64s column. 127 - 64 = 63.

What is the biggest number that goes into 63. 32. Put 1 in the 32s column. 63 - 32 = 31.

What is the biggest number that goes into 31. 16. Put 1 in the 16s column. 32 - 16 = 15.

What is the biggest number that goes into 15. 8. Put 1 in the 8s column. 15 - 8 = 7.

What is the biggest number that goes into 7. 4. Put 1 in the 4s column. 7 - 4 = 3.

What is the biggest number that goes into 3. 2. Put 1 in the 2s column. 3 - 2 = 1.

Put a 1 in the 1s column.

So we have 1111111 in binary.

Good luck.

Paul

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

Written horizontally.

128 64 32 16 8 4 2 1

1 1 1 1 1 1 1

What is the biggest number that goes into 127. 64. Put 1 in the 64s column. 127 - 64 = 63.

What is the biggest number that goes into 63. 32. Put 1 in the 32s column. 63 - 32 = 31.

What is the biggest number that goes into 31. 16. Put 1 in the 16s column. 32 - 16 = 15.

What is the biggest number that goes into 15. 8. Put 1 in the 8s column. 15 - 8 = 7.

What is the biggest number that goes into 7. 4. Put 1 in the 4s column. 7 - 4 = 3.

What is the biggest number that goes into 3. 2. Put 1 in the 2s column. 3 - 2 = 1.

Put a 1 in the 1s column.

So we have 1111111 in binary.

Good luck.

Paul

Oct 02, 2014 | Office Equipment & Supplies

This is a nice take home pseudo-coding assignment.

While Not Done;

Break the assigned tasks down & start charting.

Continue;

While Not Done;

Break the assigned tasks down & start charting.

Continue;

Apr 29, 2014 | Computers & Internet

In what follows the symbols d and b stand for decimal and binary

5d=101b

8d=1000 b

2000d=11111010000b

But write a birth date in binary? It seems to me more interesting to write a birth date in Roman numerals, or even in Egyptian or Mayan Hieroglyphics.

5d=101b

8d=1000 b

2000d=11111010000b

But write a birth date in binary? It seems to me more interesting to write a birth date in Roman numerals, or even in Egyptian or Mayan Hieroglyphics.

Oct 12, 2013 | Office Equipment & Supplies

1) Look at the following numbers before trying to convert binary to decimal. Each of them represent the value in a binary number from left to right.

128-64-32-16-8-4-2-1

2) Look at your binary number, for this example lets use 10010010. For each one add the corresponding number from step 1, the number you come out with is the conversion.

So: 10010010 -> 128+16+2 -> 146

10010010 = 146

128-64-32-16-8-4-2-1

2) Look at your binary number, for this example lets use 10010010. For each one add the corresponding number from step 1, the number you come out with is the conversion.

So: 10010010 -> 128+16+2 -> 146

10010010 = 146

Jul 03, 2011 | Office Equipment & Supplies

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