haya.Learning made clear
Internal data representation and number systems sheet
Structured-answer frame

Convert 156₁₀ into binary, octal and hexadecimal. Show your working.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Binary: divide by 2. 156→78 r0, 78→39 r0, 39→19 r1, 19→9 r1, 9→4 r1, 4→2 r0, 2→1 r0, 1→0 r1. Read the remainders upward: 10011100₂.
  2. 2 · Octal: group the bits in 3s. 010 011 100 → 2, 3, 4 → 234₈.
  3. 3 · Hexadecimal: group the bits in 4s. 1001 1100 → 9, 12 → 9C₁₆ (12 is written C).
  4. 4 · Check each answer. Octal: 2×64 + 3×8 + 4 = 128 + 24 + 4 = 156. Hex: 9×16 + 12 = 144 + 12 = 156.
  5. 5 · State the final answer. 156₁₀ = 10011100₂ = 234₈ = 9C₁₆.

Scoring tip: Always show the remainders and the check. Method marks are given even if one digit slips.