2.4b: Binary Addition & Shifts
Exam Board:
OCR
Specification:
J277
Watch on YouTube:
Binary Addition
Overflow Errors
Binary Shifts
Issues with Shifts
Binary Addition
Binary addition is a method of adding binary values without having to convert them into denary.
How to add binary numbers:
What is an overflow error?
An overflow error occurs when a binary value is too large to be stored in the bits available.
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With a byte (8 bits) the largest number that can be held is 255. Therefore any sum of two binary numbers that is greater than 255 will result in an overflow error as it is too large to be held in 8 bits.
What is binary shift?
Binary shift is used to multiply and divide binary numbers.
The effect of shifting left is to multiply a binary number.
The effect is doubled by each place that is shifted.
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The effect of shifting right is to divide a binary number.
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Shifting by 1 has an effect of 2.
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Shifting by 2 has an effect of 4.
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Shifting by 3 has an effect of 8.
For example, shifting left by 2 places has an effect of multiplying by 4.
Another example: Shifting right by 3 places has an effect of diving by 8.
How to shift a binary number:
Binary Shifts
Questo's Questions
Binary Addition:
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1. Explain what an overflow error is. [2]
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2. Add together the following binary values. If an overflow error occurs you must state one has occurred.
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a. 010110012 and 010001012 [2]
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b. 110110112 and 010111012 [2]
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c. 001101102 and 011010112 [2]
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d. 110110112 and 010101112 [2]
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e. 011011012 and 110101102 [2]
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Binary Shifts:
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1a. Draw a diagram to show the effect of multiplying and dividing a binary number. [2]
1b. Draw a diagram or table to show the effect a shift has for each place from 1 to 4. For example, a shift of 1 place has an effect of 2. [4]
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2. State the effect of the following shifts:
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a. Shift right by 2 places.
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b. Shift left by 1 place.
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c. Shift left 3 places.
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d. Shift right by 4 places. [1 each]
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3. Shift the following binary numbers and state the effect of the shift:
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a. 10101011 : Shift left by 2 places.
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b. 11101100 : Shift right by 3 places.
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c. 00001011 : Shift right by 2 places.
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d. 01101110 : Shift left by 1 place. [2 each]