 # How to convert a decimal number to binary using the Subtraction Method

Oh Like the STS if you find today’s concert to be helpful, please subscribe Share and or like in today’s tutorial We’re going to convert from a decimal to a binary number and we’re going to use what’s called a subtraction method Something to keep in mind is that the more familiar you are with the powers of two the easier of this conversion processes? So the number we’re going to convert From decimal to binary is the number 58. Let’s begin by listing our powers of two. Let’s start over here with two to the zero To two the first two to the second two to the third two to the fourth two to the fifth and Two to the sixth. All right, two to the first power. I’m sorry two to the zero power anything raised to the zero power is one two to the first is 2 2 squared is 2 times 2, which is 4 2 to the third is 2 times 2 times 2 which is 8 and we can see the process here It seems like we’re multiplying by two each time So 2 to the fourth 8 times 2 to give us 16 2 to the fifth, which would be 2 times 16 which would be 32 and 2 to the sixth which would be 32 times 2 which would be 64 so here we have our powers are 2 listed now 2 To do this process we have we’re trying to convert the number 58 So let’s look at the powers of 2 that are less than or equal to 58 So we want the highest power that’s less than or equal to 50 of 58 so here we see 64 is too much. The first one here we can use is 32 because it is less than or equal To 58. So we’re going to use 32 now. We do our subtraction. Our subtraction here is going to be 58 minus 2 32 or 8 minus 2 is 6 and 5 minus 3 is 2 So now 26 is the number that we’re looking for that we’re doing our comparison with so we see here that 64 is too much 32 is too much 16 is less than or equal to 26. So we’re going to use the number 16 and Then here we’re going to do another subtraction, which is going to be 26 – the 16 So here’s 6-6 to give us 0 and then 2 minus 1 to give us 10 now we’re using 10 for our comparison 64 is too much 32 is too much 16 is too much 8 is the next number that we can use because it’s less than or equal to 10 So we’re going to place our 8 here and now we do our subtraction 10 minus that 8 and I’ll do that here 10 – 2 8 to give us 2 again We’re looking for the number that is less than or equal to the difference that we just found too much too much too much Too much too much 2 is less than or equal to 2 So we’re going to do 2 minus 2 and again We can place this 2 up here 2 minus 2 gives us 0 and that lets us know that that we can stop now before we go ahead and do the conversion Let’s check to make sure that these powers of 2 add up to 58. So let’s do this here to the right So we have 32 Plus the 16. Well 6 plus 2 is 8 and 3 plus 1 is 4 Then I have the 8 plus 2 while 8 + 2 is 10. So I’m going to add the 10. So 48 plus 10 is 58 so I know that I did pick the correct Powers of 2 and now what I need to do is just select each one of these So we use the 32. So that means we’re going to have this power of 2 turned on We use the power of 16 that bit is turned on We use the power of 8. So this bit here is turned on and we use the power of 2 Well, we used where we have 2 so this here is turned on everywhere else We have to place a 0 so we didn’t use 2 to the 0 we didn’t use 2 to the second and we did not use 2 to the sixth So here we see that 58 is the same thing as 0 1 1 1 0 1 0 Alright, and this here is the representation of 58 in in binary format All right, that sums up this tutorial. If you found this content useful, please subscribe share alike And as always, thank you for watching

## One thought to “How to convert a decimal number to binary using the Subtraction Method”

1. Mr. Speller's Math Tutorials says:

Learn how to convert numbers from one base to another using the Division Method and Subtraction. The clips in this playlist show how to convert between decimal, binary & hexadecimal numbers. https://www.youtube.com/playlist?list=PLsX0tNIJwRTwEYqA_7a6jTo0K0Vhb6rcf