Topic 6 of 6
Check bits, binary, codes, pictures and sizes before a test
One idea at a time. Try the example, then keep going.
Big ideas · 1 of 14
Big ideas
Do this: Say what one bit and one byte mean.
A BitOne 0 or 1. The SMALLEST piece of computer data.Exactly: A binary digit: a single 0 or 1. It records the state of one switch, off or on.Mix-up alert: A bit is not a byte. It takes 8 bits to make 1 byte.See this in Key words is one 0 or 1; 8 bits make a ByteA group of 8 bits.Exactly: Eight bits handled together. One byte has 256 different patterns, enough for the numbers 0 to 255.Mix-up alert: A byte is 8 bits, not the other way round. A bit is the smaller one.See this in Key words. We use 0 for off and 1 for on. Switches can reliably be in these two states.
Do this: Read the warning. Then explain the correct idea.
A BitOne 0 or 1. The SMALLEST piece of computer data.Exactly: A binary digit: a single 0 or 1. It records the state of one switch, off or on.Mix-up alert: A bit is not a byte. It takes 8 bits to make 1 byte.See this in Key words is not a byte. One bit is one 0 or 1. A ByteA group of 8 bits.Exactly: Eight bits handled together. One byte has 256 different patterns, enough for the numbers 0 to 255.Mix-up alert: A byte is 8 bits, not the other way round. A bit is the smaller one.See this in Key words is a group of 8 bits.
Big ideas
Do this: Use the place values to read a pattern and write a number.
Binary Place valueWhat a digit is worth because of WHERE it sits.Exactly: In binary, the columns from right to left are worth 1, 2, 4, 8, 16, 32, 64 and 128. Each column is worth double the one to its right.Mix-up alert: A 1 in the 8s place is worth 8. A 1 in the 1s place is worth only 1.See this in Key words double from right to left: 1, 2, 4, 8, 16, 32, 64, 128. Left to right, a 4-bit number uses 8, 4, 2, 1.
To ConvertChange how a number is WRITTEN without changing how much it is.Exactly: Binary to decimal: add the place values that have a 1. Decimal to binary: take the biggest place value that fits, write 1, subtract, and keep going.Mix-up alert: Converting changes the writing, not the amount. 1011 in binary and 11 in decimal are the same amount.See this in Key words binary to decimal, add the place values that have a 1. Keep the place values above the digits as you work.
To ConvertChange how a number is WRITTEN without changing how much it is.Exactly: Binary to decimal: add the place values that have a 1. Decimal to binary: take the biggest place value that fits, write 1, subtract, and keep going.Mix-up alert: Converting changes the writing, not the amount. 1011 in binary and 11 in decimal are the same amount.See this in Key words decimal to binary, try each place from biggest to smallest; write 1 and subtract if it fits, otherwise write 0. Keep every position, including leading zeros.
Do this: Follow each step. Then explain the working.
Read 1101 using place values, left to right: 8, 4, 2, 1.
The total is 8 + 4 + 1 = 13.
Do this: Follow each step. Then explain the working.
Write 11 in 4 bits: places 8, 4, 2, 1.
The digits are 1011; check: 8 + 2 + 1 = 11.
Do this: Read the warning. Then explain the correct idea.
1010 in BinaryA way of writing numbers with only TWO digits: 0 and 1.Exactly: A number system where each place value is a power of two: 1, 2, 4, 8 and so on. Computers store all data in binary.Mix-up alert: 1010 in binary is ten. It is not one thousand ten.See this in Key words is not one thousand ten. Use place values 8, 4, 2, 1, left to right. Add the places with a 1: 8 + 2 = 10.
Big ideas
Do this: Say which rule gives a bit pattern its meaning.
An EncodingAn AGREED RULE that gives bit patterns a meaning.Exactly: A set of rules for turning information into bits and back again. The reader must use the same encoding as the writer.Mix-up alert: Bits do not carry their meaning inside them. The same pattern can mean different things under different encodings.See this in Key words is an agreed rule: 0110 can mean 6 as a number or right, then down as moves. Place values: 8, 4, 2, 1 give 0 + 4 + 2 + 0 = 6. Direction code: 00 up, 01 right, 10 down, 11 left. Split 0110 into 01 and 10. The reader must use the same rule as the writer.
Letters are stored as number codes; in ASCII, A is 65, written 01000001.
Do this: Read the warning. Then explain the correct idea.
Bits do not carry a meaning on their own. An EncodingAn AGREED RULE that gives bit patterns a meaning.Exactly: A set of rules for turning information into bits and back again. The reader must use the same encoding as the writer.Mix-up alert: Bits do not carry their meaning inside them. The same pattern can mean different things under different encodings.See this in Key words gives them meaning. The writer and reader must use the same rule. A pattern can mean a number under one rule and moves under another.
Do this: Explain when you may count one byte per character.
A CharacterOne letter, digit, space or symbol in text.Exactly: A single unit of text, such as A, 7, a space or a question mark. ASCII gives each character a number code. In these activities, assume one byte per capital letter: A is 65, written 01000001.Mix-up alert: A character is not always exactly one byte in real text. When a question says "assume one byte per character", that is a rule for that question.See this in Key words is not always exactly one byte in real text. In these activities, we assume one byte per capital letter. When a question says "assume one byte per character", that is a rule for that question.
Big ideas
Do this: Use the size rule to check the worked example.
A picture is a grid of PixelOne tiny square of color in a digital picture.Exactly: The smallest dot in the grid that makes up a digital image. Each pixel's color is stored as one or more bits.Mix-up alert: More bits per pixel means more possible colors, not more pixels. More stored bits do not guarantee a better-looking picture.See this in Key words; more bits per pixel give more possible colors. For black and white, use 1 bit per pixel: 0 white, 1 black.
Count PixelOne tiny square of color in a digital picture.Exactly: The smallest dot in the grid that makes up a digital image. Each pixel's color is stored as one or more bits.Mix-up alert: More bits per pixel means more possible colors, not more pixels. More stored bits do not guarantee a better-looking picture.See this in Key words data only; ignore headers (file details), padding (extra space) and compression (ways to shrink files).
For PixelOne tiny square of color in a digital picture.Exactly: The smallest dot in the grid that makes up a digital image. Each pixel's color is stored as one or more bits.Mix-up alert: More bits per pixel means more possible colors, not more pixels. More stored bits do not guarantee a better-looking picture.See this in Key words data only, width × height × bits per pixel ÷ 8 gives bytes; ignore headers, padding and compression. Round the total up to whole bytes only when the bits do not divide evenly by 8.
Round up to a whole ByteA group of 8 bits.Exactly: Eight bits handled together. One byte has 256 different patterns, enough for the numbers 0 to 255.Mix-up alert: A byte is 8 bits, not the other way round. A bit is the smaller one.See this in Key words only when the total bits do not divide evenly by 8. Round the total, not each row.
Do this: Follow each step. Then explain the working.
A picture is 12 × 8 pixels at 8 bits per pixel. Pixel data only: ignore headers, padding and compression.
The pixel data needs 96 bytes; no rounding is needed.
Do this: Explain why file size alone cannot tell you how good a picture looks.
A bigger picture file is not always a better picture. Storage sizeHow much space data takes up, measured in bits, bytes, KB, MB or GB.Exactly: 8 bits make 1 byte. In this course, 1 KB is 1,000 bytes, 1 MB is 1,000 KB and 1 GB is 1,000 MB. Some computers count 1,024 instead of 1,000. For picture calculations, count pixel data only: ignore headers, padding and compression. Divide the total bits by 8 and round up to whole bytes only if they do not divide evenly.Mix-up alert: A bigger file is not always a better picture. Size depends on the number of pixels, the bits per pixel and the file format.See this in Key words depends on the number of pixels, the bits per pixel and format choices. More stored bits do not guarantee a better-looking picture.
Big ideas
Do this: Say how a computer stores sound. Then put the storage units in order.
A computer measures a sound wave many times a second and stores each measurement as a number written in BitOne 0 or 1. The SMALLEST piece of computer data.Exactly: A binary digit: a single 0 or 1. It records the state of one switch, off or on.Mix-up alert: A bit is not a byte. It takes 8 bits to make 1 byte.See this in Key words. More measurements follow the wave more closely and take more storage.
Using more BitOne 0 or 1. The SMALLEST piece of computer data.Exactly: A binary digit: a single 0 or 1. It records the state of one switch, off or on.Mix-up alert: A bit is not a byte. It takes 8 bits to make 1 byte.See this in Key words for each sound measurement records it more precisely and also takes more storage.
From smallest to largest: bit → byte → KB → MB → GB.
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Checklist
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Practice conversions, bits and bytes, bit patterns and picture sizes. For pictures, count pixel data only. Keep going as long as you like.
Streak: 0 correct in a row. This session only.
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| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
Self-test
Do this: Choose an answer, then read the explanation. Return to the checklist for anything you need to study.
16 questions. One at a time.
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Checklist
Do this: Explain each idea without looking. Go back to the lesson for any unchecked box.
Self-test
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5 questions. One at a time.
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Match
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