Binary numbers and conversion

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Notes de leçon Diapos Questions d'entraînement

Notes de leçon

Why binary?

Digital circuits reliably distinguish two logic levels, represented as 0 and 1. Patterns of bits can encode numbers, text, images and sound.
The on/off switch picture is a simple model; actual logic levels correspond to defined voltage ranges.

Two logic states

Units

A bit is one binary digit; a nibble is four bits and a byte is eight.
Using decimal prefixes: kB = 1,000 bytes, MB = 1,000,000 bytes, and each larger SI prefix is a factor of 1,000. Binary prefixes KiB, MiB and GiB instead use factors of 1,024.

Place values (8-bit)

128, 64, 32, 16, 8, 4, 2, 1.

Reading unsigned 1011

Converting binary to denary

Add the place values where there is a 1. 1011 = 8 + 2 + 1 = 11. 11001010 = 128 + 64 + 8 + 2 = 202.

Converting denary to binary

Subtract place values or divide by 2. 13 = 8 + 4 + 1 = 1101. Pad with zeros to 8 bits: 00001101.

Range

n bits can store 2ⁿ different values: 8 bits → 256 (0 to 255); 16 bits → 65,536.

Patterns and unsigned range

Uses

Understanding binary is needed for storage, networking and data representation.

Diapos

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Questions d'entraînement

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1.What is a bit?
Easy
- Aa binary digit
- Ba byte
- Ca number
- Da letter
2.How many bits are in a byte?
Easy
- A8
- B4
- C16
- D2
3.How many bits are in a nibble?
Easy
- A4
- B8
- C2
- D16
4.How many different values can 8 bits store?
Easy
- A256
- B255
- C128
- D8
5.What is the largest unsigned eight-bit integer?
Easy
- A255
- B256
- C128
- D127
6.What is 0101 in denary?
Easy
- A5
- B3
- C7
- D10
7.What is 1111 in denary?
Easy
- A15
- B16
- C8
- D14
8.What is unsigned binary 10000000 in denary?
Easy
- A128
- B64
- C255
- D256

Plus de questions

9.What is 9 in binary (4 bits)?
Easy
- A1001
- B1100
- C0110
- D0011
10.What is 13 in binary (4 bits)?
Easy
- A1101
- B1011
- C1110
- D0111
11.What is 1 kilobyte (using 1000)?
Easy
- A1,000 bytes
- B100 bytes
- C10 bytes
- D1,000,000 bytes
12.What is 11001010 in denary?
Medium
- A202
- B203
- C198
- D172
13.What is 45 in 8-bit binary?
Medium
- A00101101
- B00101011
- C01011010
- D10110100
14.What is 200 in 8-bit binary?
Medium
- A11001000
- B11000100
- C10011000
- D11100000
15.How many values can 4 bits represent?
Medium
- A16
- B8
- C4
- D15
16.What is the largest unsigned four-bit integer?
Medium
- A15
- B16
- C8
- D7
17.Which is bigger: 1 MB or 1 GB?
Medium
- A1 GB
- B1 MB
- Cequal
- Dcannot tell
18.What is the minimum number of bits needed to represent 300 distinct values?
Medium
- A9
- B8
- C10
- D12
19.What is the denary value of 00010110?
Medium
- A22
- B24
- C18
- D26
20.Which unsigned binary number is largest?
Medium
- A11000000
- B10111111
- C01111111
- D10000000
21.If a file is 2,000,000 bytes, how many megabytes is it (using 1000)?
Medium
- A2
- B20
- C200
- D0.2
22.What is the binary for 255 in 8 bits?
Medium
- A11111111
- B11111110
- C10000000
- D01111111
23.What is the least significant bit?
Easy
- Athe rightmost bit
- Bthe leftmost bit
- Cthe middle bit
- Da parity bit
24.What is the most significant bit?
Easy
- Athe leftmost bit
- Bthe rightmost bit
- Cthe middle bit
- Da check bit
25.Using decimal prefixes, how many gigabytes make one terabyte?
Medium
- A1,000 times bigger
- B100 times bigger
- C10 times bigger
- Dthe same
26.What base does binary use?
Medium
- A2
- B10
- C16
- D8
27.Computers use binary because circuits have two states.
Easy
True or false?
28.One byte is 8 bits.
Easy
True or false?
29.Eight bits can represent every unsigned integer from 0 through 256.
Easy
True or false?
30.1011 in binary equals 11 in denary.
Easy
True or false?
31.Binary uses digits 0 to 9.
Medium
True or false?
32.Which are units of data?
Medium
- Abit
- Bnibble
- Cbyte
- Dkilobyte
- Ecentimetre
33.Which binary numbers equal 5?
Medium
- A101
- B0101
- C00000101
- D5 in base 2
- E110
34.Convert the denary number 37 to 8-bit binary, showing your working.
Medium

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