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Intro to CS 9-10 / Week 09 / Monday
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Week 09 · Bits and Binary

Monday

Only two symbols
// Place values, one byte, overflow, and sampling a smooth curve
⏱ about 20 min

Monday: Only Two Symbols

Comet wants Beacon to send the morning water reading, 75, to mission control. "Easy," she says. "Just send 75."

Wren points at the relay screen. "Our relay link only sends two kinds of pulse: on and off."

"Two symbols?" Comet says. "How do you send 75 with only two symbols?"

Nova hovers over the bench and projects a row of eight little lights. Some glow and some stay dark.

"Every number Beacon stores is already made of these," she says. "Would you like a hint? Each light is worth a different amount."

Wren leans closer. "What do you notice about the amounts?"

Comet counts along the row. "They double. One, two, four, eight..."

Bits and bytes

This week asks: how can only 0s and 1s stand for numbers, letters, colors and sound?

Computing devices store data digitally. That means the smallest parts of any value are bits.

Bit is short for binary digit. A bit is either 0 or 1. A byte is 8 bits.

Binary place values

Binary, or base 2, uses only combinations of the digits 0 and 1.

As in our everyday base 10 numbers, a digit's position decides what it is worth.

Each position's place value is the base raised to the power of the position. Positions are numbered from 0 at the right.

So in binary, the place values from the right are 1, 2, 4, 8, 16, 32, 64 and 128. Each one doubles the one before.

Position76543210
Place value1286432168421

To read a binary number, add the place values wherever there is a 1. The binary number 0101 has 1s in the 4 and 1 places, so it is 5.

READ SMALL BINARY NUMBERS
  • Read the question.
  • Tap your answer.
What is the binary number 1001 in base 10?
What is the binary number 1111 in base 10?
What is the place value of position 4?
How many bits are in one byte?
StatementTrue or false?
A bit is either 0 or 1.?
Binary uses the digits 0 through 9.?
Binary positions are numbered starting from 0 at the right.?
Each binary place value is double the one to its right.?
WHY THIS EXERCISEThese four facts are all you need to read any binary number.
Bit is short for binary ____.
A group of 8 bits is called a ____.
Binary is also called base ____. Write the number as a word.
Try it
Count from 0 to 7 in binary using three fingers: a raised finger is 1, a folded finger is 0.
Your right-hand finger is worth 1, the next 2, the next 4. Can you show 5 and 6?
For a grown-up
This week, your student learns how computers store numbers, letters and colors as 0s and 1s, using paper cards.
Everything is unplugged. No lesson asks your student to open an app, a website or an AI tool.
On paper, draw eight boxes labeled 128, 64, 32, 16, 8, 4, 2 and 1. Shade boxes to show 5, then 9, then 15 in three rows.
WHICH IS BIGGER?
  • Read the question.
  • Tap your answer.
Which binary number is bigger: 1000 or 0111?
One 1 in position 7 is worth more than 1s in positions 0 to 6 together. True?

Good start, developer. Tomorrow you will turn readings into binary and back.