Binary, Denary & Data Units – Quick-Review Notes

Denary (Decimal) Number System

• Purpose: everyday human counting.
• Base: $10$.
• Digits: ${0,\dots,9}$.
• Place-value headings: $10^3,10^2,10^1,10^0$ (Thousands, Hundreds, Tens, Units).
• Example: $2493=2\times10^3+4\times10^2+9\times10^1+3\times10^0$.

Binary Number System

• Purpose: internal language of computers (switches ON/OFF).
• Base: $2$.
• Digits: ${0,1}$.
• Place-value headings: $2^7,2^6,2^5,2^4,2^3,2^2,2^1,2^0$.
• Example: $00011000<em>2=16+8=24</em>{10}$.

Denary vs Binary (Quick Contrast)

• Number of digits: denary $10$ | binary $2$.
• Powers used: $10^n$ | $2^n$.
• Typical use: people | computers.

Data-Storage Units (Decimal Prefixes)

• Bit (b): stores a single $0$ or $1$.
• Byte (B): $8$ bits.
• Kilobyte (KB): $1000$ bytes.
• Megabyte (MB): $1000$ KB.
• Gigabyte (GB): $1000$ MB.
• Terabyte (TB): $1000$ GB.
• Petabyte (PB): $1000$ TB.
• Order (small → large): bits < Byte < KB < MB < GB < TB < PB.

Converting Between Units

• Bits ↔ Bytes: multiply/divide by $8$.
• Adjacent decimal prefixes: multiply/divide by $1000$.
  • Example: $2.5$ GB → $2.5\times1000=2500$ MB.
  • Example: $1850$ KB → $1850/1000=1.85$ MB.
  • Example: $500$ B → $500/1000=0.5$ KB.

Typical File Sizes (Guideline)

• Plain text (.txt): bytes to low $\text{KB}$.
• Word-processed document: $\text{KB}$–low $\text{MB}$.
• Web image: $\text{KB}$–low $\text{MB}$.
• MP3 audio: $\text{MB}$.
• HD video: $\text{GB}$.

Fast Checks & Examples

• Floppy-disk question: $1$ GB = $1000$ MB; $1000/1.44 \approx 694.44$ → need $695$ disks.
• Unit ordering prompt: GB bits MB Byte PB TB KB → correct sequence: bits, Byte, KB, MB, GB, TB, PB.

Key Takeaways

• Remember: computers think in $2$, humans think in $10$.
• Storage growth pattern: every step up is $\times1000$ (decimal) except bits↔bytes which is $\times8$.
• Master quick conversions for exam speed: multiply to grow, divide to shrink; attach units each time.