Binary: the language of computers

§Text Passage

1Summary 重點摘要

Computers only understand 0 and 1. One 01 is a bit; eight bits make a byte — just enough to store one English letter.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Why computers use only 0 and 1A computer circuit most reliably distinguishes two states: current on (1) and off (0). With only two states, a signal survives slight interference and still reads clearly as 0 or 1, and the circuitry stays simple, reliable and cheap; telling ten states apart directly invites errors. So a computer stores everything in binary: text, images, sound and video all become strings of 0s and 1s before storage. It is the same logic as a light switch, which is merely on or off.
2. Counting in binaryDecimal carries at ten; binary carries at two: the binary sequence 1, 10, 11, 100, 101, 110, 111, 1000 corresponds to decimal 1 through 8. The crucial point is that binary '10' means two, not ten — the classic error — so always state the base, writing 1011₂ or 'binary 1011' in words. In an exam answer, omitting the base leaves '10' ambiguous between two and ten and costs marks directly. Labelling the base is the first rule of binary questions.
3. Binary to decimal: place valuesConvert by multiplying each digit by its place value and adding; from the right the values run 1, 2, 4, 8, 16 — the powers of two. For binary 1011 the digits from the right are 1, 1, 0, 1, so 1×1 + 1×2 + 0×4 + 1×8 = 11, meaning 1011₂ = 11 in decimal. A quick check on place values: the rightmost place is always 1 and each step left doubles it. Beginners often reverse the place values left-to-right and ruin the whole sum; writing the place values right-to-left before starting is the safest routine.
4. Bits, bytes and file sizesOne 0 or 1 is a bit; eight bits make one byte, just enough to store one English letter. Upward: 1024 bytes = 1 KB, 1024 KB = 1 MB, 1024 MB = 1 GB, 1024 GB = 1 TB — each step is 1024 times, not 1000. For everyday scale: a phone photo runs 2 to 5 MB, a song about 4 MB, and an hour of video counts in GB, which is why a 128 GB phone fills up quickly — one reason cloud storage and streaming keep growing in popularity.
5. Beyond numbers: text, images and soundBinary stores more than numbers. Text uses code tables — ASCII writes capital A as 65 (binary 01000001), and typing A records exactly that string of 0s and 1s. An image is a grid of pixels, each colour stored as a number, so a megapixel camera saves a million values; sound is sampled as loudness numbers at tiny intervals. Every medium ends as 0s and 1s, differing only in the encoding — and that is why copying a file loses nothing at all.
6. Decimal to binary: divide by two, take remaindersThe reverse uses repeated division by 2: divide the number by 2, note each remainder, stop when the quotient reaches 0, then read the remainders bottom-up. For 13: 13 ÷ 2 = 6 remainder 1; 6 ÷ 2 = 3 remainder 0; 3 ÷ 2 = 1 remainder 1; 1 ÷ 2 = 0 remainder 1; read bottom-up as 1101, the binary form of 13. Verify with place values: 1×8 + 1×4 + 0×2 + 1×1 = 13. The two methods invert each other — answering with one and checking with the other is the safest combination in an exam.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• The computer world is only 0s and 1s (bits)
• 8 bits = 1 byte, roughly one English letter
• Units: KB → MB → GB → TB, each 1024 times bigger
• Text, images, sound and video are all stored in binary
• Conversion trick: place values 1, 2, 4, 8 from the right — multiply, then add