Binary Numbers and Place Value
Counting with two digits, where each column is worth twice the column to its right. Converting both ways between binary and decimal.
What a learner can do afterwards
- Convert an 8-bit binary number to decimal
- Convert a decimal number below 256 into 8 bits
- State the largest value 8 bits can hold, and why that is the limit
1 · Read
You already met bits: wires that are either on or off, standing for 1 or 0. One such digit is the smallest piece of information a computer holds. Line several up in a row and the pattern can hold a number, the kind used to score a game or count your steps. Three wires can track three lightbulbs, one on-off choice each.
Each column to the left is worth double: 1, 2, 4, 8, 16, and on. To read 1101, add the columns holding 1, which gives 8 + 4 + 1 = 13. Your turn: 37 is 32 + 4 + 1, written 100101.
To write a decimal number in binary, divide by 2 again and again and read the remainders upward. Eight bits make a byte, and a byte holds 0 to 255. That makes 255 the largest value 8 bits can hold, since 256 would need a ninth bit.
Write the place values above the digits and cross out the zeros. Then add only what is left.
Bits are on-off digits, columns double leftward, and 8 bits hold 0 to 255.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.