Starter quiz
- Match the terms to the description.
- binary⇔a number system using 0 and 1 ✓
- decimal⇔a number system using the digits 0 to 9 ✓
- transistor⇔a switch in an electronic circuit ✓
- instruction⇔a direction for performing a task ✓
- What number system uses only the digits 0 and 1?
- decimal
- binary ✓
- octal
- hexadecimal
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- What is the base of the decimal number system?
- 2
- 8
- 10 ✓
- 16
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- What is a carry in binary addition?
- a number that is discarded
- a digit that remains unchanged
- a subtraction result
- a value moved to the next column ✓
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- What is the result of the binary addition 1 + 1?
- '10' ✓
- What is the result of the binary addition 11001 + 111?
- '100000' ✓
Exit quiz
- Match the terms with their descriptions
- left shift⇔multiplies by powers of 2 ✓
- right shift⇔divides by powers of 2 ✓
- overflow⇔when memory capacity is exceeded ✓
- underflow⇔when digits are rounded down as they drop near zero ✓
- What is an overflow in binary operations?
- a number that is too small to process
- a number that fits perfectly in memory
- a number that is negative
- a number that is too large to be represented ✓
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- Which of the following can cause overflow?
- adding two large numbers ✓
- subtracting two small numbers
- multiplying by zero
- dividing by one
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- In binary, what is 11001 × 10?
- '110010' ✓
- In binary, what is 11001 ÷ 100?
- '110' ✓
- What should be considered when storing binary multiplication results?
- The result can be any size.
- The result is always zero.
- The result must fit within the allocated memory. ✓
- The result is always negative.
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Worksheet
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Presentation
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Video
Lesson Details
Key learning points
- Binary shifting is shifting the bits to the left or to the right.
- If you shift to the left, you multiply the number by a power of 2.
- If you shift to the right, you divide the number by a power of 2.
- Overflow is when a number is too large to be stored in allocated memory.
- Underflow is when a number is too small to be processed.
Common misconception
When performing binary multiplication any result can be stored, regardless of how many binary digits are needed.
The size of a binary number that can be stored is allocated in memory. Sometimes the result of a binary shift may result in a larger binary number that can be stored in the number of bits available.
Keywords
Binary shifting - when binary digits are moved left or right, multiplying or dividing them by powers of 2
Overflow - when a number is too large to be represented in the available binary digits
Underflow - when a number is too small to be represented in the available binary digits
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