WorksheetsCS Edexcel 2.1b Signed Binary Numbers (Two's Complement)
Total questions: 18
Worksheet time: 9mins
What is the leftmost bit used for in sign and magnitude representation of binary numbers?
To determine the type of operation to perform
To store additional information about the number
To indicate the magnitude of the number
To represent the sign of the number (positive or negative)
How do you convert a positive binary number into its negative equivalent using two's complement?
Invert the bits and add 1
Add 1 and then invert the bits
Subtract 1 and then invert the bits
Leave the bits unchanged
The range of values represented by a byte in two's complement is (a)
In two's complement, how do you convert a negative number back to positive?
Subtract 1 and flip the bits
Add 1 and invert the bits
Leave it unchanged
Flip the bits only
What is the result of adding -5 (in two's complement) and 5?
-5
5
-10
0
If the second number in a subtraction is larger than the first, you can infer that the result will be (a)
How should you interpret a two's complement result that is negative?
Add it to the maximum value of the byte
Leave it as is, it is already understandable
Convert it back to positive to understand the value
What is the binary representation of the number 5 using sign and magnitude?
(a)
What is a drawback of using sign and magnitude for binary numbers?
It cannot represent positive numbers
It makes addition difficult
It uses too much memory
It is not compatible with decimal numbers
Match the following binary numbers with their two's complement representation.
0 0 0 0 0 0 0 0
Two's complement of 0
1 0 0 0 0 0 0 0
Two's complement of -128
0 1 1 1 1 1 1 1
Two's complement of 127
1 1 1 1 1 1 1 1
Two's complement of -1
What is the first step in converting a positive binary number to a negative using two's complement?
Add one
Flip the bits
Subtract one
Multiply by -1
Why is it beneficial to represent numbers using two's complement?
It makes subtraction easier
It allows for larger numbers
It makes addition work correctly
It simplifies multiplication
Using two's complement, what is the decimal equivalent of the binary number 11111110 after flipping the bits and adding one?
-1
-2
-3
0
What is the main issue with logical binary shifts when used with signed binary values?
The signed bit (MSB) is lost.
The number becomes zero.
The number doubles in size.
The number remains unchanged.
What is the key difference between arithmetic shifts and logical shifts?
Arithmetic shifts retain the signed bit (MSB).
Arithmetic shifts double the number.
Arithmetic shifts lose the signed bit (MSB).
Arithmetic shifts make the number zero.
The type of binary shift that should be used with signed binary numbers to retain the signed bit is (a)
The result of an arithmetic right binary shift on the two’s complement binary value 10101010 is (a)
Arithmetic left binary shifts do not consistently work on signed two’s complement binary values because:
They can cause overflow errors.
They are slower than right shifts.
They do not change the sign bit.
They require more processing power.
