How do iworkout how to convert base 10 numbers to binary

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

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

base eight is not binary binary is base 2 think of an odometer where when each number gets to 7 it goes back to 0 and the next one goes up one. There are settings on a windows calculator to convert from decimal to octidecimal, hexidecimal etc

Dinary? Never heard that one before. What is a dinary number? Anyway your calculator cannot perform the operations. The Casios can work in Binary (base 2), Octal (base 8), Decimal (base 10) and Hexadecimal (base 16). Some Sharps can do calculations in base 5 (pental).

You can't. It can only convert integral numbers to binary base, but not fractions.

Letters can be converted into decimal number using ASCII table. Every Character has it own equivalent number. Once converted into decimal (base 10), I could be easily converted into binary (base 2)
You could also use applications or web based applications such as ASCII to binary converter to help you convert it.

If you're already in decimal mode, press SHIFT BIN to switch to binary mode.

To convert a number from decimal to binary, press MODE 4 to switch to BASE-N mode. You'll find yourself in decimal mode. Enter the number to convert, press =, then press SHIFT [BIN] (the log key) and see the number in binary. To convert another number, press SHIFT [DEC] to return to decimal, enter the number, press =, then press SHIFT [BIN]. An analogous process works for hexadecimal and octal as well.

To return to "normal" use, press MODE 1 for COMP mode or MODE 2 for complex mode.

Press MODE 4 to enter the BASE-N mode. Type in the decimal number, then press BIN to convert to binary. Press DEC to switch back to decimal for the next conversion.

You're limited to numbers in the range [-32768...32767] in binary. You can extend the range if you convert to octal or hexadecimal and then mentally convert each digit to three or four bits.

Press MODE 4 to enter the BASE-N mode. If the display doesn't say Dec, press SHIFT DEC (the x^2 key) to set base 10. Enter the number to convert. Press SHIFT BIN (the log key) to switch to base 2.

Each time you switch the base the current value is redisplayed in that new base.

dear kladofora thire is no 4:BASE-N in the mode please i need help Gist