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AQA GCSE · Question 02.3 · Fundamentals of data representation
The arithmetic effect of applying a left binary shift of two to a binary number is to multiply that number by four.
State the arithmetic effect of applying a left binary shift of four to a binary number.
The arithmetic effect of applying a left binary shift of two to a binary number is to multiply that number by four.
State the arithmetic effect of applying a left binary shift of four to a binary number.
How to approach this question
A left binary shift of 'n' places is arithmetically equivalent to multiplying the number by 2^n.
In this question, the shift is four places to the left, so n=4.
The effect is to multiply the number by 2^4.
Calculate 2^4: 2 * 2 * 2 * 2 = 16.
Full Answer
Multiply the number by 16.
A left binary shift (also known as a logical shift left) moves all bits in a binary number to the left by a specified number of places. For each place shifted, the number is effectively multiplied by 2.
Therefore, a left shift of 'n' places has the arithmetic effect of multiplying the original number by 2^n.
In this case, n = 4.
So, the effect is multiplication by 2^4, which is 16.
Common mistakes
✗ Stating division instead of multiplication.
✗ Calculating 2*4=8 instead of 2^4=16.
✗ Confusing left shift with right shift (which is division).
Practice the full AQA GCSE Computer Science Paper 2
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