Bits and Bytes CS Thinking Example 1

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Example 1

easy
How many different values can be represented with 3 bits? List all possible 3-bit binary patterns.

Solution

  1. 1
    Step 1: Each bit can be 0 or 1. With 3 bits, the number of combinations is 23=82^3 = 8.
  2. 2
    Step 2: The patterns are: 000, 001, 010, 011, 100, 101, 110, 111.
  3. 3
    Step 3: These represent the values 0 through 7 in decimal. In general, n bits can represent 2n2^n different values.

Answer

8 different values (0 to 7): 000, 001, 010, 011, 100, 101, 110, 111.
A bit is the smallest unit of data (0 or 1). The number of possible values doubles with each additional bit: 1 bit = 2 values, 2 bits = 4, 3 bits = 8, and so on.

About Bits and Bytes

A bit is a single binary digit (0 or 1), the smallest unit of digital data. A byte is a group of 8 bits that can represent 256 different values (0 to 255), enough to encode one text character. All digital storage and communication is measured in bits and bytes.

Learn more about Bits and Bytes →

More Bits and Bytes Examples

Example 2 medium

Convert between storage units: (a) How many bytes in 2 kilobytes? (b) A file is 3,145,728 bytes — ho

Example 3 medium

An image is 800 × 600 pixels. Each pixel uses 24 bits (8 bits each for red, green, blue). What is th

Example 4 hard

A colour system uses 4 bits per colour channel (red, green, blue). (a) How many shades can each chan

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