Computer Science

Computer Science LESSON ON Number Base Subtraction and Simple Equations John Owen, Rockport Fulton HS

Objective • In this lesson you’ll learn how to do subtraction and how to solve simple equations involving Base 2, 8, and 16. • Again, it is essentially the same concept as Base 10, just in a different base! John Owen, Rockport Fulton HS

Review Base Ten Subtraction • In Base 10 subtraction, you use a very simple process. • Look at this problem: 48 -37 = 11 John Owen, Rockport Fulton HS

Review Base Ten Subtraction 48 -37 = 11 • Each column is subtracted to get an answer of 11…pretty easy, huh? John Owen, Rockport Fulton HS

Subtraction, Base 10 • Now look at this problem: 63 -37 • In this problem, you need to borrow. John Owen, Rockport Fulton HS

Subtraction, Base 10 513 63 -37 • Borrowing means taking a value from the next column and adding it to the column you need. John Owen, Rockport Fulton HS

Subtraction, Base 10 513 63 -37 • In this case, borrow from the 6, which becomes five, and add 10 to the 3, making 13. John Owen, Rockport Fulton HS

Subtraction, Base 10 513 63 -37 • When you borrow 1 from one column, it becomes the value of the base in the next column, or 10 in this case. John Owen, Rockport Fulton HS

Subtraction, Base 10 513 63 -37 26 • Then you subtract the two columns with a result of 26. John Owen, Rockport Fulton HS

Subtraction, Base 8 • Now let’s try base eight: 63 -37 • Again, in this problem, you need to borrow. John Owen, Rockport Fulton HS

Subtraction, Base 8 511 63 -37 • Borrow from the 6, which becomes five, and add 8 to the 3, making 11! John Owen, Rockport Fulton HS

Subtraction, Base 8 511 63 -37 • When you borrow 1 from a column, it becomes the value of the base in the next column, or 8 in this case. John Owen, Rockport Fulton HS

Subtraction, Base 8 511 63 -37 24 • Then you subtract the two columns with a result of 24, base 8. John Owen, Rockport Fulton HS

Subtraction, Base 16 Now base 16: 519 63 -37 • Again, we borrow from the 6, which becomes five, and add 16 to the 3, making 19! John Owen, Rockport Fulton HS

Subtraction, Base 16 519 63 -37 • When you borrow 1 from a column, it becomes the value of the base in the next column, or 16 in this case. John Owen, Rockport Fulton HS

Subtraction, Base 16 519 63 -37 2C • In the ones column, 19 minus 7 is 12, which is C in base sixteen, with 2 in the second column. John Owen, Rockport Fulton HS

Subtraction, Base 16 Here’s another example in base 16 D6 -3B • How is this one solved? Try it. John Owen, Rockport Fulton HS

Subtraction, Base 16 C22 D6 -3B • We must borrow from D, which becomes C, then add 16 to 6, which makes 22. John Owen, Rockport Fulton HS

Subtraction, Base 16 C22 D6 -3B 9B • 22 minus B (11) is B. • C minus 3 is 9. • Answer is 9B John Owen, Rockport Fulton HS

Subtraction, Base 2 Now base 2: 11 - 1 10 • This one is easy…answer is 10 John Owen, Rockport Fulton HS

Subtraction, Base 2 Another in base 2: 02 110 - 1 • Here we need to borrow from the twos place… John Owen, Rockport Fulton HS

Subtraction, Base 2 02 110 - 1 101 Subtract to get the answer. John Owen, Rockport Fulton HS

Subtraction, Base 2 Still another in base 2: 02 110 - 11 1 Now borrow again… John Owen, Rockport Fulton HS

Subtraction, Base 2 2 100 - 11 11 Final answer is 11, base 2 John Owen, Rockport Fulton HS

Simple Equations Here an equation to solve (base 10): x + 6 = 14 John Owen, Rockport Fulton HS

Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = 8 John Owen, Rockport Fulton HS

Simple Equations Now do it in base 8: x + 6 = 14 John Owen, Rockport Fulton HS

Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = ? John Owen, Rockport Fulton HS

Simple Equations Answer is 6, base 8 12 x + 6 = 14 -6 -6 x = 6 John Owen, Rockport Fulton HS

Simple Equations Here’s an equation in base sixteen (remember, A and F are NOT variables, but base sixteen values): x + 2A = F3 John Owen, Rockport Fulton HS

Simple Equations Solution? x + 2A = F3 John Owen, Rockport Fulton HS

Simple Equations Subtract 2A from both sides: E19 x + 2A = F3 - 2A-2A x =C9 John Owen, Rockport Fulton HS

Exercises • Now try these exercises • 12 - 12 = • 78 - 68 = • F16 - A16 = • 158 - 68 = • 4916 - 2B16 = • CC16 - AD16 = John Owen, Rockport Fulton HS

Exercises • 738 - 348 = • 3E16 – 2F16 = • 1012 - 102 = • 11012 - 112 = • 10102 - 1112 = • 7168 - 3648 = • 7768 + 3378 = John Owen, Rockport Fulton HS

Exercises Now let’s mix it up a bit! • AE16 + 768 = _________8 • 2348 + 110110112 = _________16 • 101102 - F16 + 768 = _________10 • 38 + 3910 - 1101012 = _________16 • 11112 - F16 + 1510 = _________16 John Owen, Rockport Fulton HS

Exercises And finally, some equations • x16 + 7616 = AB16 • x2 - 10112 = 1012 • x8 + 568 = 728 • x2 + 2510 = 1F16 • x8 + 3748 - 65568 = BAD16 • 378 + X16 = 110111102 John Owen, Rockport Fulton HS

ANSWERS (JUMBLED) John Owen, Rockport Fulton HS

Computer Science