Presenting Conversions in a Report

In an assignment, a conversion is marked on three things:

• 1Method — did you use a correct method and show each step?
• 2Accuracy — is the final answer right?
• 3Presentation — can the marker follow your working easily?

A correct answer with no working may lose marks. A clear method with a small slip usually keeps most of the marks.

For each conversion, use this order. The example uses a different number from any assignment question — use it as a model, not as an answer.

Convert 171₁₀ to binary, octal and hexadecimal.

(a) Decimal → binary (repeated division by 2)

Reading the remainders from bottom to top: 171₁₀ = 10101011₂

(b) Binary → octal (groups of 3 from the right)

8 bits → one leading zero added: 010 101 011 → 253₈

(c) Binary → hexadecimal (groups of 4 from the right)

1010 1011 → A B → AB₁₆

Check: 10101011₂ = 128 + 32 + 8 + 2 + 1 = 171 ✓

• Convert it back. Turn your answer into decimal with place values. It should match the number you started with.
• Estimate the size. 171 is between 128 and 256, so its binary form must have 8 bits. If you get 7 or 9 bits, something is wrong.
• Look at the digits. A binary answer may only contain 0 and 1; an octal answer only 0–7. A hex answer from an even decimal number must end in an even digit (0, 2, 4, 6, 8, A, C, E).