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Topic 4—Computing mathematics and logic


This topic is primarily the representation of real numbers and Boolean logic

(All Topic 4 Instructional Video links together on one page.)

4.1—Number Systems and Representations

4.1.1 Calculate in the bases specified in 3.5.3.
(And a non-pdf with sample questions.)
          video review part 1 - conversions
          video review part 2 - adding in hexadecimal
          video review part 3 - 2s complement

4.1.2 State the mantissa and exponent of a binary number in floating-point representation.
Relate this to scientific notation in decimal.

          for video review see next section

4.1.3 Apply binary notation to represent real numbers.
(And a non-pdf with sample questions.)
Representing negative real numbers in binary - notes picture.
          video review part 1 - fixed point representation
          video review part 2 - floating point - positive numbers
          video review part 3 - floating point - negative numbers
          video review part 4 - largest and smallest magnitude & precision

4.1.4 Discuss the advantages and disadvantages of integer and floating-point representations.

4.1.5 Define truncation error, underflow error, and overflow error.

4.1.6 Outline three situations, with each one providing an example of when and where one of the errors in 4.1.5 can occur. Each situation should show a different error, that is all three errors should be described.

 

4.2—Boolean Logic

4.2.1 Define the Boolean operators and, or, not, nand, nor, and xor, by drawing appropriate truth tables.
          (video review combined with next section)

4.2.2 Construct Boolean expressions using the operators in 4.2.1.
          video review - operators & expressions

4.2.3 Calculate the values of Boolean expressions using truth tables.
          (video review combined with next section)

4.2.4 Convert Boolean expressions into simpler forms.
          video review truth tables & reducing expressions

4.2.5 Construct a simple logic circuit that corresponds to a given Boolean expression by using standard logic gates.
          (video review combined with next section)

4.2.6 Construct a Boolean expression that corresponds to a given logic circuit.
(And a non-pdf with sample questions.)
          video review conversion between circuit diagrams and expressions

4.2.7 Explain the function of a given circuit.