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Decimal to Binary

Decimal-to-binary conversion works by systematically determining which powers of two fit into a given value. This foundational skill underpins how computers represent and process numeric data.

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About this video

Binary and decimal are two different numbering systems used to represent the same values, and converting between them is a fundamental skill in computing and networking. Decimal uses base 10, meaning each digit position represents a power of 10, while binary uses base 2, where each bit position represents a power of 2. Understanding how to move between these systems builds the foundation for working with IP addressing, data storage, and low-level system operations. The conversion process works by testing descending powers of two against a target decimal number. Beginning with 128 and working down through 64, 32, 16, 8, 4, 2, and 1, each power is assigned a binary digit of 1 if it is less than or equal to the remaining value, or 0 if it exceeds it. When a 1 is placed, that power's value is subtracted from the remainder, and the process continues until the full number has been accounted for. Applying this method to the decimal number 103 yields the binary equivalent 01100111, confirming that the same quantity can be expressed accurately in either system.

What you'll learn

Convert a decimal integer to its 8-bit binary equivalent using the positional subtraction (place value) method

What's covered

Decimal to Binary Conversion

Decimal Number Example
- One block of 100
- Three single blocks
- Total value 103
Binary Place Values
- 128 place
- 64 place
- 32 place
- 4, 2, 1 places
Conversion Process
- Check if place value fits
- Subtract and find remainder
- Repeat for each position
Conversion Result
- 103 decimal
- 01100111 binary

Aligned to

CompTIA Tech+

1.1 Compare and contrast notational systems.

1.3 Illustrate the basics of computing and processing.

Key terms

Decimal: The base-10 number system using digits 0–9; the standard system used in everyday counting and arithmetic, and the most common format for presenting numeric output to humans.
Binary: The base-2 number system that uses only the digits 0 and 1; the native language of digital computers, which store and process data as electrical on/off states.
Bit: Short for binary digit, the smallest unit of data in computing, holding a single value of 0 or 1; all digital information is ultimately composed of bits.
Place Value: The weight assigned to a digit based on its position within a number; in binary, each position represents a successive power of 2 (1, 2, 4, 8, …), making position the key to decoding binary values.
Positional Subtraction Method: A technique for converting a decimal number to binary by testing each power of 2 from largest to smallest and subtracting it when it fits into the remaining value.

Transcript

Let's use our blocks to figure out how to convert from a decimal system to a binary system. So what we're going to do is we're going to start out with the decimal system here. And how much do we have? Well, we have one block of 100, and so that's 100, and we've got three one blocks, and so that's three. So 100 + 3 is 103.

Now let's convert that to binary. And the answer is still going to be 103, it's just we're going to allocate it a little differently. So what does that look like? Well, we can start with this 128 and say, is 128 larger than 103? And yes it is, so there's no 128 inside of this. Is 64 larger? No, it's not, so there's a 64, there's 64 blocks in 103. So what we can do is we can actually take that out of this and put it down here, and what that leaves us left over here is 39, 39 blocks left.

So do I have a 32 inside of the 39? Yes, 32 is not larger, it's smaller, so I can take out 32 blocks and I can put it right there. So now I have 011 so far. So then what I have left here is seven blocks. So if I count them up, I've got four, five, six, seven.

So is there a 16 in there? Nope, that's a larger number. Is there eight? Nope, that's a larger number. Is there a four? Yes, there is, I've got a four inside my seven here, so I can take four of them out, put them there. I've got three left. Is there two in there? Well, there certainly is, so I've got that now. And there's one left, that can go right there.

So now what I've just done is I've converted it now from my 103 in decimal to a 01100111.

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