Mon Prof Augmenté
Reading a Binary Switch Panel
Age 18 · Computer Science
A row of four switches stands for a binary number, where each switch is worth double the one to its right. A switch that is on adds its value to the total, and a switch that is off contributes nothing, so 1011 works out to 8 + 2 + 1 = 11.
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In the picture
- The glowing bulb above the first switch: it marks a 1 in that column, so that column’s value is counted.
- The lever of the second switch, pointing down: it marks a 0, so the 4 belonging to that column stays out of the total.
- The engraved plate reading 8: place values double from right to left, giving 1, 2, 4, 8.
- The pencilled slip reading 11: the sum 8 + 2 + 1 is the decimal value of the binary number 1011.
Examples
- A colour channel in a photo editor runs from 0 to 255 because eight binary places add up to 255 at most.
- File permissions written as 755 come from three bits each, where read, write and execute are worth 4, 2 and 1.
Key takeaways
- Each binary place is a power of two, doubling as you move left: 1, 2, 4, 8, 16.
- The decimal value is the sum of the place values whose digit is 1.
Quiz: Reading a Binary Switch Panel (Age 18)
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What decimal value does the binary number 1101 stand for?
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A fifth switch is added to the left of a four-switch panel. What is that new column worth?
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On a four-switch panel, only the leftmost switch (worth 8) and the rightmost switch (worth 1) are on. What decimal value does the panel show?
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