In this series tutorial I'll be explaining how to convert between binary, hexadecimal, and decimal without the use of a computer. For the sake of this tutorials length I'm only going to explain how to do bytes of information, IE 0-255, 00000000-11111111, and 00-FF.
The first thing you need to know about this, is what they are. They're different number systems computers use to store/display/communicate information. Decimal is a base 10 number system, meaning it uses 10 different numbers for each numerical place. (0-9) Binary has two numbers used (0 and 1) and hex uses 16. Hex uses 0-9 plus A-F to represent 10-15.
BINARY TO DECIMAL
This is probably the easiest conversion in the set. The easiest way to do this I've found, is to number off eight places like so
The number under each space represents what number in decimal it represents. For example
Since this only has a 1 over the 32, this equals 32 in decimal. Yadig? To do numbers with more than one place all you have to do is add them up! For instance:
128 + 64 + 16 + 2 + 1 = 211
Easy, huh?
DECIMAL TO BINARY
Now that you've done binary to decimal, decimal to binary is going to be a lot easier to understand. We'll use the same number layout as before, we'll just be working backwards.
Let's take the number 142 for example. Simply all we do is take the largest number that goes into our starting number from it. For example, since the largest number there is 128, and 128 goes into 142, we will have a 1 in the eighth space in our binary number. Next, we take 142 and subtract 128 from it, getting 14.
So, now that we have the first number done, lets check the next few numbers. 64 is definitely larger than 14, so we'll leave that space 0, along with 32 and 16. However, 8 does go into 14, so the fourth binary digit is a 1. Take away 8 from 14, and we get 6. 4 Goes into 6, which leaves 2, and 2 goes into 2, making the third and second digits both ones. The first digit is zero, as the decimal number is 0.
This leaves 10001110 as the binary conversion of 142!
As you do this more you'll start to memorize what place is what number in decimal, and will be able to do it in your head. If you want to do bigger numbers, simply double the last number and add that place. For example, the ninth binary digit represents 256 in decimal, the tenth 512, and so on.
I'll be making more threads on decimal/hex and binary/hex. I meant to finish the series a long time ago but I stopped because I'm a lazy asshole. I'll finish it if anyone is interested.
Leave feedback please btw.
The first thing you need to know about this, is what they are. They're different number systems computers use to store/display/communicate information. Decimal is a base 10 number system, meaning it uses 10 different numbers for each numerical place. (0-9) Binary has two numbers used (0 and 1) and hex uses 16. Hex uses 0-9 plus A-F to represent 10-15.
BINARY TO DECIMAL
This is probably the easiest conversion in the set. The easiest way to do this I've found, is to number off eight places like so
The number under each space represents what number in decimal it represents. For example
Since this only has a 1 over the 32, this equals 32 in decimal. Yadig? To do numbers with more than one place all you have to do is add them up! For instance:
128 + 64 + 16 + 2 + 1 = 211
Easy, huh?
DECIMAL TO BINARY
Now that you've done binary to decimal, decimal to binary is going to be a lot easier to understand. We'll use the same number layout as before, we'll just be working backwards.
Let's take the number 142 for example. Simply all we do is take the largest number that goes into our starting number from it. For example, since the largest number there is 128, and 128 goes into 142, we will have a 1 in the eighth space in our binary number. Next, we take 142 and subtract 128 from it, getting 14.
So, now that we have the first number done, lets check the next few numbers. 64 is definitely larger than 14, so we'll leave that space 0, along with 32 and 16. However, 8 does go into 14, so the fourth binary digit is a 1. Take away 8 from 14, and we get 6. 4 Goes into 6, which leaves 2, and 2 goes into 2, making the third and second digits both ones. The first digit is zero, as the decimal number is 0.
This leaves 10001110 as the binary conversion of 142!
As you do this more you'll start to memorize what place is what number in decimal, and will be able to do it in your head. If you want to do bigger numbers, simply double the last number and add that place. For example, the ninth binary digit represents 256 in decimal, the tenth 512, and so on.
I'll be making more threads on decimal/hex and binary/hex. I meant to finish the series a long time ago but I stopped because I'm a lazy asshole. I'll finish it if anyone is interested.
Leave feedback please btw.
