Binary Systems for Integer Numbers

Typical tasks:

• Conversion between bases (signed/unsigned integers, decimal, hex)
• Conversion between fixed-point numbers base-2 and base-10
• Identifying range and overflows of integer types in C

Examples:

• Convert (12.50)10 to binary (answer: 1100.1)

  (12.50)10

• Convert −65 to signed 8-bit (answer: 10111111)

  −65

• Convert 11011010 to hex (answer: 0xDA)

• Convert the signed char 11011010 to decimal (answer: −38)

  −38

• Convert the unsigned char 11011010 to decimal (answer: 218)

  218

• What is the range of signed/unsigned integers with n bits?

  n

• What is the hex encoding of MAX_INT, MIN_INT, 1, 0, 1, MAX_UINT, MIN_UINT?

• What is the size and range of the C types char, short, int, long?

• What are the conditions to detect signed overflow?

• What are the conditions to detect unsigned overflow?

Floating-Point Numbers

Typical tasks:

• Explaining the use and size of fields in the IEEE 754 encoding (32 bits, 64 bits, or “classroom 12-bit”)
• Convert a number encoded as IEEE 754 to decimal