Number Systems for Computing: Binary, Hexadecimal, Bit Flags, Two's Complement, Fixed & Floating Point and Storage Units

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn a sensor reading into binary by dividing by 2 again and again, read the remainders as bits, and turn an 8-digit binary text back into a decimal number with MID and POWER.
• Write a status byte as two hex digits and as 8 bits through a nibble lookup table, split a display colour code into its red, green and blue values, and write the same byte in octal.
• Split six status bytes into eight yes/no flags, count the devices with a low battery, set the alarm bit on one device and clear the update bit on another – without double-counting a bit that is already set.
• Work out the signed range of 8-, 16- and 32-bit values, store negative sensor offsets as bytes from 0 to 255 and decode bytes from a log back into signed values.
• Find the largest unsigned value for common bit widths, the bits a value needs, what a full counter shows after more events, and how many packets arrived when an 8-bit counter has rolled over.
• Find the resolution of a sensor that sends sixteenths of a degree, store six temperatures as integers, decode them again and measure the rounding error each one picks up.
• Decode the exponent and mantissa fields of 8-bit toy floating-point patterns, turn a pattern into its value, and find the nearest value the format can store for 0.1.
• Explain why a 512 GB drive shows less, size a raw camera snapshot in KiB, decode one character of a display message through a code table and work out how many bytes the message needs with the shortest fixed-length code.