Binary Numbers: Count with Zero and One
Understand that binary uses only two digits, that each place is worth double the one to its right, and that n bits can represent 2 to the power n different values.
Before you try
What if you only had two fingers to count with? How high could you go?
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What happened?
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Eight lamps hold whole numbers from 0 to 255 only. Real computers use many more bits, and need extra rules for negative numbers and decimals.
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Try these ideas
- Flip the 128, 32 and 1 lamps and read the sum line.
- Set the value to 7 and press +1 to watch the carry ripple.
- Switch to 4 bits and find the largest number you can show.
Why it works
We usually count in tens because each place is worth ten times the one to its right: units, tens, hundreds. Computers count in twos, because a switch is either on or off and that is easy to build reliably. In binary each place is worth double the one to its right: 1, 2, 4, 8, 16, 32, 64, 128. To read a binary number you simply add up the place values whose switches are on.
Adding one works the same way as in tens, except you carry at two instead of ten, so 0111 plus 1 rolls three places over to zero and lights the next one, giving 1000. Eight bits, called a byte, give 256 different patterns, numbered 0 to 255, which is exactly enough for every letter, digit and symbol in basic text. This simulator lets you flip bits, set a decimal value, add one and watch the carry ripple.
Check your understanding
Question 1 of 4
What is the binary number 1011 in decimal?
Each place in a binary number is worth how much compared with the one to its right?
How many different values can 8 bits represent?
What is 0111 plus 1 in binary?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
For parents & teachers
- Count from 0 to 15 on four fingers, treating each finger as a bit.
- Ask why a computer file size is measured in bytes.
- Write your age in binary and compare with a friend.