APDR

Number and Data Representation Lab

Algorithms, Programming, and Data Representation · Module 92313 · Chapter 3

Predict first, then reveal. Convert numbers, decode bit patterns, read character codes, and trace binary arithmetic.

How the lab works

  1. Predict. Commit to an answer before the stage moves.
  2. Rate your confidence. A sure but wrong answer is useful; it appears under Your results.
  3. Watch the reveal. Follow the conversion or bit steps, then use the link to review the matching guide section.
  4. Explore. Finish an experiment to open its controls and tick its lab skill.

3.1 Number systems: convert and group digits

Positional notation uses the same place-value rule in every base. Group binary digits in threes for octal and in fours for hexadecimal.

Digits are grouped from the right · base range 2–16

Convert a numeral

Result: —

3.2 Integer representations: decode the pattern

A bit pattern has no signed meaning until its encoding is specified. Keep the width fixed while comparing unsigned, signed, biased, and BCD forms.

The same bits can name different values

Choose an encoding

Value or BCD: —

3.3 Character data: read ASCII codes

ASCII assigns code values to characters. This sandbox decodes printable ASCII bytes; byte sequences outside ASCII need their character encoding identified first.

The first 128 Unicode code points correspond to ASCII

Decode ASCII bytes

Text: —

3.4 Unsigned arithmetic: trace the operation

Carry and borrow move between binary columns. Multiplication forms partial products; division must leave a remainder smaller than its divisor.

Columns run right to left, with carries or borrows above

Try binary arithmetic

Result: —

3.5 Two’s complement: check the fixed-width result

Negation and subtraction use fixed-width bit patterns. Decode the stored result and compare the exact answer with the range to detect signed overflow.

Carry-out and signed overflow are different checks

Calculate at a fixed width

Stored pattern: — · decoded value: — · carry out: — · overflow: —

Your results

Personal study lab based on the APDR Chapter 3 study guide and supplied lecture notes. The ASCII sandbox covers printable ASCII-range bytes and does not infer a general byte encoding. Not an official FAU publication; check course details against the current materials. Made by Thanate Amornjiraporn (Focus).