Give the main drawback of sign and magnitude representation.

Sign and magnitude has two representations of zero, 00000000 and 10000000. Arithmetic also needs extra logic, because the signs must be compared before adding.

How is a negative number written in two's complement?

The positive value is written in binary, every bit is inverted, and 1 is added. The most significant bit then carries a negative place value.

Write −45 in 8-bit two's complement.

Denary 45 is 00101101, which inverts to 11010010. The addition of 1 gives 11010011, which is 211 minus 256, or −45.

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Number Systems and Binary Arithmetic

Two's complement and sign and magnitude

3 things to know
Component 2

Overview

The two ways of writing a negative number in a fixed-length store, their ranges, the two representations of zero that one of them suffers, and why arithmetic is easier in the other.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How is a negative number written in sign and magnitude form?

Key term

Write −45 in 8-bit sign and magnitude.

Key term

State the range of 8-bit sign and magnitude representation.

Questions from this subtopic

Each one with the model answer underneath.

1
How is a negative number written in sign and magnitude form?
Model answer
The most significant bit is used as a sign, with 0 for positive and 1 for negative. The remaining bits hold the magnitude as an ordinary binary number.
2
Write −45 in 8-bit sign and magnitude.
Model answer
Denary 45 is 0101101 in seven bits. With a sign bit of 1 the full pattern is 10101101.
3
State the range of 8-bit sign and magnitude representation.
Model answer
8-bit sign and magnitude covers −127 to +127. The seven magnitude bits reach 127 and the sign bit chooses the direction.
4
Give the main drawback of sign and magnitude representation.
Model answer
Sign and magnitude has two representations of zero, 00000000 and 10000000. Arithmetic also needs extra logic, because the signs must be compared before adding.
5
How is a negative number written in two's complement?
Model answer
The positive value is written in binary, every bit is inverted, and 1 is added. The most significant bit then carries a negative place value.
6
Write −45 in 8-bit two's complement.
Model answer
Denary 45 is 00101101, which inverts to 11010010. The addition of 1 gives 11010011, which is 211 minus 256, or −45.

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