Exam practice
Every question from the end of every unit, with hints and answers to open. After you check an answer, mark how you did, and come back to the ones you didn’t get.
13 questions
Unit 5 · Zeros and Ones
Explain the meaning of these words: bit, byte, binary, pixel, resolution.
Answer
- Bit: a binary digit, 0 or 1; the smallest piece of information a computer stores.
- Byte: a group of 8 bits. It can hold one English letter or a number from 0 to 255.
- Binary: the number system with only two digits, 0 and 1, whose place values double from right to left (1, 2, 4, 8…). Computers store everything in binary.
- Pixel: one of the tiny squares a picture on a screen is made of; short for picture element.
- Resolution: the number of pixels across and down a picture, such as 32 × 32. A higher resolution gives a sharper picture but needs more bits.
Why do computers use binary, only 0 and 1? Give two reasons.
Answer
- A computer is made of switches (transistors), and a switch has two states, on and off, which fit 1 and 0 exactly.
- Two states are easy to tell apart, so the computer rarely makes mistakes: a small wobble in the electricity can’t turn “on” into “off”, while with ten levels close together it could turn one digit into another.
(Also: switches with two states are simple, small, cheap and fast to make.)
Change these binary numbers into decimal: i. 101 ii. 1100 iii. 10011 iv. 11111111
Answer
- i.101 = 4 + 1 = 5
- ii.1100 = 8 + 4 = 12
- iii.10011 = 16 + 2 + 1 = 19
- iv.11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
Change these decimal numbers into binary: i. 6 ii. 9 iii. 20 iv. 31 v. 100 vi. 200
Hint
Take the biggest place value that fits (1, 2, 4, 8, 16…), subtract it, and carry on with what is left.
Answer
- i.6 = 4 + 2 = 110
- ii.9 = 8 + 1 = 1001
- iii.20 = 16 + 4 = 10100
- iv.31 = 16 + 8 + 4 + 2 + 1 = 11111
- v.100 = 64 + 32 + 4 = 1100100
- vi.200 = 128 + 64 + 8 = 11001000
Write the numbers from 0 to 8 in binary. What do you notice about the numbers 1, 2, 4 and 8 in binary?
Answer
0 = 0, 1 = 1, 2 = 10, 3 = 11, 4 = 100, 5 = 101, 6 = 110, 7 = 111, 8 = 1000.
1, 2, 4 and 8 are each a single 1 followed by zeros (1, 10, 100, 1000), because each is exactly one place value. In decimal, 1, 10, 100 and 1000 look the same way for the same reason.
Copy and complete the table.
| Number of bits | Number of patterns | Biggest number |
|---|---|---|
| 2 | 3 | |
| 3 | 8 | |
| 4 | ||
| 8 |
Answer
| Number of bits | Number of patterns | Biggest number |
|---|---|---|
| 2 | 4 | 3 |
| 3 | 8 | 7 |
| 4 | 16 | 15 |
| 8 | 256 | 255 |
The biggest number is always one less than the number of patterns, because one pattern (all 0s) is used for 0.
Draw an 8 × 8 grid and color it from these bits (1 = black, 0 = white). What is the picture?
00000000 · 00011000 · 00111100 · 01111110 · 11111111 · 01000010 · 01011010 · 01011010
Answer
A house: a roof that gets wider from row 2 to row 5, then the two walls (the 1s near each end of rows 6 to 8), and a dark door in the middle (the 11 in rows 7 and 8).
A black-and-white picture is 40 pixels across and 30 pixels down.
- i.How many pixels does it have?
- ii.How many bits does it take?
- iii.How many bytes?
Answer
- i.40 × 30 = 1,200 pixels.
- ii.One bit for each pixel: 1,200 bits.
- iii.1,200 ÷ 8 = 150 bytes.
A memory card holds 16 GB. A song takes about 4 MB. About how many songs can it hold? (Use 1 GB = 1,024 MB.)
Answer
16 GB = 16 × 1,024 MB = 16,384 MB.
16,384 ÷ 4 = 4,096 songs, about four thousand.
Sita says her internet is “10 Mbps”, so a 10 MB video will arrive in one second. Is she right? Explain.
Answer
No. Mbps is megabits per second (small b), but MB is megabytes (big B), and a byte is 8 bits. 10 Mbps is about 10 ÷ 8 = 1.25 MB each second, so a 10 MB video takes about 10 ÷ 1.25 = 8 seconds, eight times longer than she thinks (a little more in real life, as a connection rarely runs at full speed).
Arrange from smallest to biggest: 1 GB, 1 bit, 1 TB, 1 KB, 1 byte, 1 MB.
Answer
1 bit, 1 byte, 1 KB, 1 MB, 1 GB, 1 TB.
Here is a black-and-white picture, 5 pixels across and 5 down (■ is black, □ is white). Write its bits, one row at a time, using 1 = black and 0 = white. What letter is it?
■ □ □ □ ■■ □ □ □ ■■ ■ ■ ■ ■■ □ □ □ ■■ □ □ □ ■Answer
10001 · 10001 · 11111 · 10001 · 10001. It is the letter H: 25 pixels, so 25 bits.
Choose the most sensible unit (bytes, KB, MB, GB or TB) for the size of each of these, and say why.
- i.a short text message
- ii.a photo from a phone’s camera
- iii.a full-length film
- iv.all the storage in a phone
Answer
- i.Bytes: a short message is a few dozen letters, and each English letter takes one byte.
- ii.MB: a phone photo is a few million bytes, a few megabytes.
- iii.GB: a full-length film is usually around one or a few gigabytes, depending on its quality.
- iv.GB: phones hold tens or hundreds of gigabytes (a few dear ones hold 1 TB).