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Representing unsigned integers inside a computer

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• Unsigned numbers inside the computer
  • Computer use the "binary number system" positional system to represent unsigned numbers.

  • The Binary number system:
    • Uses 2 digits: 0 and 1 (represented by the switch position: off and on)

    • Value of the n^th digit before the decimal is equal to 2ⁿ

  • Examples:

    Unsigned value 4 bit binary number 8 bit binary number -------------- ------------------- ------------------- 0 0000 00000000 1 0001 00000001 2 0010 00000010 3 0011 00000011

• Converting a Binary Representation to a Decimal Representation
  • Question:

    Given a binary number representation an unsigned value, how to determine the decimal number representation represented ?

  • Answer:

    Sum the value of each digit multiplied by its place value

  • Example:

    Given the binary representation: 01011001 What is the decimal representation for the same unsigned value ? Solution: ========= Digits: 0 1 0 1 1 0 0 1 Place values: 128 64 32 16 8 4 2 1 -------------------------------- 64 + 16 +8 + 1 = 89 Answer: 89

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• Converting a Decimal Representation to a Binary Representation

  • Question:

    Given a decimal number representation an unsigned value n, how to determine the binary number representation represented ?

  • Answer:

    Find "factors" 2k in the value n This can be achieved by divide the number n repeatedly by 2 and collect the remainder in the reverse order.

  • Example:

    Given the unsigned decimal representaion 89 What is the binary representation in 8 bits (1 byte) for the same unsigned value ? Solution: ========= 89 /2 ------ 1 <--- remainder of 89/2 44 <--- quotient of 89/2 /2 ------ 0 <--- remainder of 44/2 22 <--- quotient of 44/2 /2 ------ 0 11 /2 ------ 1 5 /2 ------ 1 2 /2 ------ 0 1 /2 ------ 1 0 <----- Done Binary number: 1011001 (7 bits) Pad to 8 bits: 01011001 Answer: 01011001