Data Representation using Signed Magnitude (1)

Binary Number Representation

• There are four ways to represent binary numbers:

  • Unsigned Magnitude

  • Signed Magnitude

  • 1's Complement

  • 2's Complement

Unsigned Magnitude

• Can only represent positive binary numbers.

  • For example:

    • +6 is represented as 110.

    • Cannot represent -6 in this format since it only handles positives.

Signed Magnitude

• Can represent both positive and negative numbers.

• Positive number representation:

  • Example: +6 is represented by its magnitude.

    • Magnitude of 6 = 110

    • Add an extra bit (sign bit): 0 for positive.

  • Therefore, +6 in signed magnitude is 0110.

• Negative number representation:

  • Example: -6 uses the same magnitude but a different sign bit:

    • +6 = 110 (magnitude)

    • Add a sign bit of 1 (indicating negative).

  • Thus, -6 in signed magnitude is 1110.

Sign Bit Importance

• The sign bit determines positivity or negativity:

  • 0 = Positive

  • 1 = Negative

• It splits the representation into two parts:

  • Sign bit dictates the sign.

  • Remaining bits represent the magnitude.

Additional Examples

• To represent +13:

  • Magnitude = 1101

  • Sign bit = 0 (for positive).

  • Therefore, +13 is 01101.

• For -13:

  • Magnitude = 1101

  • Sign bit = 1 (for negative).

  • Therefore, -13 is 11101.

Range of Signed Magnitude

• The range for signed magnitude is:

  • From -2^(n-1) + 1 to 2^(n-1) - 1

  • Where n is the number of bits used.

  • For n=4:

    • Range: From -7 to +7.

      • Calculation:

        • Min: - (2^3 - 1) = -7

        • Max: 2^3 - 1 = 7

Homework Problems

• 1st Problem: Represent +5 and -5.

• 2nd Problem: Represent +9 and -9.

• 3rd Problem: Represent +16 and -16.

• Use signed magnitude representation for all problems.