Chapter 25 - The Binary Number System

Question 1

Define Two’s Complement

Answer 1

A method of working with signed binary values

Question 2

How do you add / subtract Two’s Complement numbers?

Answer 2

Just add as normal.

Calculate binary equivalent of positive number, calculate binary equivalent of negative number, then add together.

Question 3

What is fixed point?

Answer 3

Where the decimal / binary point is fixed within a number.

Question 4

What is floating point?

Answer 4

Where the decimal/binary point can move within a number.

Question 5

What are the advantages of using floating point?

Answer 5

• much wider range of numbers can be produced with the same number of bits as the fixed point system
• floating point lends itself to applications where a wide range of values may need to be represented.

Question 6

What are the advantages of using fixed point?

Answer 6

• Any hardware configured to work with integers, can be used on reals; this makes fixed point faster than floating as there is no processing required to move the binary point.
• Absolute error will always be the same meaning precision is retained albeit within a more limited range.
• Suited to applications where is speed is more important than precision
• Suited to applications where an absolute level of precision is required

Question 7

What is signed binary?

Answer 7

Binary with a positive or negative sign.

Question 8

What is overflow and underflow?

Answer 8

Overflow is when a number is too large to be represented with the number of bits allocated.

Underflow is when a number is too small to be represented with the number of bits allocated.

Question 9

What is the mantissa and exponent?

Answer 9

Mantissa is the significant digits that make up a number

Exponent is the ‘power of’ part of a number indicated how far a binary point should be shifted left or right.