4.2: Signed Binary
Exam Board:
Eduqas / WJEC
Specification:
2020 +
What is Sign and Magnitude and Two's Complement?
Sign and Magnitude and Two's Complement are both methods of writing positive and negative binary values.
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Sign and Magnitude is simpler but will cause incorrect answers if used in binary calculations.
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Two's Complement is more complex but will generate correct answers when used in binary calculations.
Sign & Magnitude
The most significant bit (MSB) is the largest bit of a binary number  the one furthest to the left.
The MSB is the sign  it represents whether the binary value is positive or negative.
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If the sign is 0 then the binary number is positive.
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If the sign is 1 then the binary number is negative.
The other bits represent the magnitude  the value of the binary number.
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For an 8bit binary number, the range is 127 to 127, because only 7 bits are used to define the magnitude.
Sign & Magnitude: Problems
Sign and magnitude is not commonly used by computers for two main reasons:â€‹
Performing binary addition and subtraction (see section 4.3) will often cause a wrong result.
In the example below, 7 + 3 should equal 4 but the result given is 2.
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Sign and magnitude creates two different values for 0  positive 0 and negative 0 which is incorrect.
Two's Complement
Two's complement is a method of representing positive and negative binary values.
It is used often by computers because binary calculations will work correctly and there is only one value for zero.
Two's Complement: Denary to Binary
To represent a negative value using two's complement follow these steps:
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Write out the positive value in binary.

Start on the righthand side and move along, copy all 0s until you get to the first 1. The first 1 is copied too.

After the first 1 invert each value (change to its opposite). So 0 becomes 1 and 1 becomes 0.
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2.
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Two's Complement: Binary to Denary
To convert a binary number to denary using two's complement you must remember that the MSB is a negative value.
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Just add the numbers with 1 together to work out the denary value.
Questo's Questions
4.2  Signed Binary:
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Sign & Magnitude
1. Using sign and magnitude, convert the following values to denary:

a. 00011101

b. 11100011

c. 10110110

d. 01001111 [1 each]
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2. Using sign and magnitude, convert the following values to binary:

a. 83

b. 13

c. 102

d. 24 [1 each]
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3. Describe two problems when using sign and magnitude. [4]
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4. Using sign and magnitude, the range of numbers that can be represented in 6 bits is from  31 to + 31. State the range of numbers that can be represented using sign and magnitude in the following bits:

a. 8 bits

b. 4 bits [1 each]
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Two's Complement
1. Using two's complement, convert the following values to binary:

a. 20

b. 49

c. 87

d. 113 [2 each]
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2. Using two's complement, convert the following values to denary:

a. 10110010

b. 11101110

c. 01101011

d. 10011111 [2 each]