# How to convert Decimal numbers into Binary numbers?

What in this thread is unclear?

I do not understand his reasoning.

What he is saying is that 156 = 128+16+8+4.
Convert that last part to binary and you get:
10000000+10000+1000+100 = 10011100.

He says take the 2^n below the number you are converting. in this case, 128 (is 2^7).
Subtract. 156 - 128 = 28.
The power of 2 below 28 is 16.
Subtract. Leaves 12.
12 = 8 + 4.

So 156 = 128 + 16 + 8 + 4.

2 Likes

@bjoern.gumboldt TNX and would you suggest the most effictive souce and book to get the most beneficial data for this topic:" [convert Decimal numbers into Binary numbers?]
best regards

The best source imho is this site. Just practice and talk about it here.

Try 127 and see what happens.
What numbers are easy for you and when does it become more difficult?

2 Likes

It also helps to memorize (common) factors of 8 and 16.
And it helps to memorize common exponents base 8 and 16.
So 8^n and 16^n where n = 2, 3, etc.

2 Likes

Here are 10 random numbers below 1000.
Just convert these to binary.
Try via octal and try via hexadecimal to see which method works best.
Octal means you get 3 binary digits in one go and hexadecimal means 4 digits.

An example via hexadecimal. Let’s convert 175.
Via hexadecimal means you first convert to hexadecimal and then to binary.

175_{10} = (10*16+15)_{10}.
10_{10} = A_{16} and
15_{10} = F_{16}

In short, 175_{10} = AF_{16}

A_{16} = 1010_{2} and F_{16} = 1111_{2}

so:
AF_{16} = 1010\ 1111_{2}

175
695
559
19
457
54
843
767
654
425

1 Like