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Diploma in Higher Education Studies

Adding binary numbers

HES 102 · Mathematics for University Study — Week 7 of 16

CourseHES 102
Week7 of 16
SemesterI
TutorOnline in the course chat

This week’s topics

Adding binary numbers

  1. The rules of binary addition
  2. Carrying
  3. Overflow

What you will be able to do

  • 1.4 Perform simple binary addition.

Activity

Add pairs of 8-bit binary numbers and spot the overflows.

Study materials

Further resources

  • Contemporary Mathematics, 4.4: Addition and Subtraction in Base Systems · PDF · OpenStax Contemporary Mathematics (2023), 4.4: the rules of binary addition and carrying, pp. 300–314 · for registered students
  • Introduction to Computer Science, 5.3: Carry and addition · PDF · OpenStax Introduction to Computer Science (2024), 5.3 on binary addition, carry and fixed-size integers, pp. 205–210 · for registered students
  • The Elements of Computing Systems, ch. 2: Boolean Arithmetic · PDF · Nisan & Schocken, The Elements of Computing Systems 2e, ch. 2 (2nd ed.): binary addition, carries and overflow; 12 pp. · for registered students
  • Understanding integer overflow in C/C++ · Open-access article · Dietz et al. (2012), International Conference on Software Engineering (ICSE). What happens in real programs when binary arithmetic overflows. · for registered students
Materials marked “for registered students” open in the student portal, which is set up as soon as you receive final acceptance.
Week 6Midterm
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Course plan
  • Week 1: Fractions, decimals and percentages
  • Week 2: Calculating with percentages
  • Week 3: Percentage increase and decrease
  • Week 4: Percentages in business: profit, mark-up and VAT
  • Week 5: Binary numbers
  • Week 6: Hexadecimal numbers
  • Week 7: Adding binary numbers
  • Midterm: Midterm evaluation
  • Week 9: Using formulae
  • Week 10: Solving equations and rearranging formulae
  • Week 11: Logic gates and truth tables
  • Week 12: Averages and range
  • Week 13: Reading charts and tables
  • Week 14: Solving problems step by step with flowcharts
  • Week 15: Review and coursework completion
  • Final: Final assessment and submission
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