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TechKnowSurge Catalog Videos DEMO: Counting in Binary, Part 2
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DEMO: Counting in Binary, Part 2

Incrementing a binary number means identifying what value comes next by adding 1 and applying carry operations across the bit positions. This skill builds on basic binary counting and is essential for working with binary arithmetic.

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About this video

Binary counting from zero is a useful starting point, but practical work with binary numbers often requires starting at an arbitrary value and determining what comes next. Incrementing a binary number means adding 1 to the least significant bit and handling any carry that results, repeating that carry propagation across each bit position until the operation resolves. This process is straightforward when the least significant bit is 0, but requires careful column-by-column work when a sequence of 1s triggers a carry chain. A clear example of this carry behavior appears when incrementing 0111. Adding 1 to the rightmost bit produces a sum of 2, which cannot be represented in a single bit, so that position resets to 0 and a carry moves left. The same resolution occurs at each successive bit position until the carry reaches an empty column, yielding 1000. Recognizing this pattern and executing it reliably across varying binary values is a foundational skill for binary arithmetic, digital logic, and low-level computing concepts.

What you'll learn

What's covered

Binary Counting: Next Number

Aligned to

CompTIA Tech+
1.1 Compare and contrast notational systems.
1.3 Illustrate the basics of computing and processing.

Key terms

Binary Number
A number expressed in base-2 using only the digits 0 and 1, where each position represents a power of two.
Binary Addition
The arithmetic process of adding two binary numbers using base-2 rules, where 0+0=0, 0+1=1, 1+1=10 (sum 0 carry 1), and 1+1+1=11 (sum 1 carry 1).
Carry
In binary addition, the value of 1 passed to the next higher bit position when a column's sum exceeds the maximum value representable by a single bit.
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.

Transcript

Another thing that's going to be really important is not just the count, but knowing what the next number is going to be. In our last exercise we started at zero and just started counting up, but that's a little different than starting in the middle somewhere and saying what the next number is. So we're going to start out with a binary number and figure out what the next number coming after that is.

In this exercise we have a number that's presented to us, and we're going to say what the next number is going to be. So let's do a couple of these.

For this first one I'm going to just count up to the next number, so essentially I'm adding 1 to it. What's going to happen is 1 plus 0 is 1, and then we carry down the other bits. So the answer to this, the next one after 1000, is going to be 1001.

Let's do another one. This next one here I'm going to add one to it as well. So what's the next one? Well, this first one cancels out, so then I carry the 1 to the next column. I add that together and that is going to be two, which we can't do, so it cancels out, we get a zero, and then I carry one to the next one. I do the same thing here, so that's going to be 0 as well, and I'm going to carry 1 to the next one. Now I've got 1000. So the next one after 0111 is going to be 1000.

There are other problems here. Go through and figure out what the answers are, what the next number is for each one of these numbers. Then check your work and make sure it's all correct.

Once again, you'll want to practice this and make sure you're familiar with it. If you're in the booklet, or if you're on my online course, you'll have some extra examples that you can go through and test out your ability of doing this. But just make sure that you have this down before you proceed on to the next step.

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