How to Read Binary

Base 10: How we normally count

We normally count by 10s, also called base 10 or decimal. You know how it works. Ten digits 0 through 9. When we count up to 9, then the next number has to move into the tens place and becomes 10. At 99 both places are full, so the next number moves into the hundreds place and becomes 100.

What is important here is that each place is a power of 10.

So each digit tells you how many of that place you have. 900 means 9 "100s" or 9 × 100.

Of course, you don't really think this way when you look at a number, but it's an important concept to understand as you learn binary.

Base 2: Binary

Binary is base 2. It only has two digits, 0 and 1. Instead of counting by 10s, binary counts by 2s. Just like in decimal where each place is a power of 10, in binary each place is a power of 2.

Counting works the same way, you just run out of digits much sooner. You have 0, then 1, and then you're out of single digits. Thus, two is written 10. Three is 11, and then both places are full, so four moves into the next place and becomes 100. Easy, right?

Try binary 11011. Just remember that each digit is a power of 2.

Got it? Here's a joke to test you:

There are only 10 kinds of people in the world: those who understand binary and those who don't.

Baby Steps: Binary-Coded Decimal (BCD)

Binary-coded decimal makes the clock easy to read. It splits the time into its tens and ones, just like the digits on a regular clock, and writes each digit separately in binary.

BCD is usually shown vertically. Each digit gets its own column with the 1 at the bottom and 2, 4, and 8 stacked above it. Each cell is a binary bit, and a bit is either off (0) or on (1). For binary clocks, the lit cells are the bits that are on.

Here is 56 seconds with the red on bits showing their decimal value instead of just their binary 1.

Note that the tens column never needs an 8, because the tens digit for minutes and seconds never goes above 5. Bennett Binary Clock has options to show or hide these unused cells, as well as options to show binary values vertically or horizontally.

True Binary: Time for your big boy pants

True binary doesn't split the number into tens and ones. The whole number is written in binary, left to right just like decimal with the biggest place on the left and the 1s place on the far right.

In binary, minutes and seconds go up to 59, so they need six bits: 32, 16, 8, 4, 2, and 1. Here is the same 56 seconds, which in binary is 111000:

It gets to be a chore adding up big numbers, so don't be ashamed to stick with BCD, especially if you're new to binary. I've been using binary clocks for decades, and even I still prefer BCD over true binary. Bennett Binary Clock lets you choose either one.

Also, don't forget about Bennett Binary Clock's awesome tap zones that can toggle displaying bit labels or decimal time if you need help or want to verify your reading.

Test Yourself

Here's a sample Bennett Binary Clock in full screen mode. It shows the current time in binary-coded decimal. Read it, then show the answer to check your binary prowess. Turn on bit labels if you need a hint.