Chapter 2: Coding numbers into binary

Question 1

What are unsigned integers?

Answer 1

unsigned because we do not let these have a sign (either negative or positive). With 4 bits, there are 16 different unique combinations. Therefore 4 bits can represent unsigned integers from 0 to 15.

Question 2

What is ones compliment?

Answer 2

This is when all the bits in a binary number are inverted

Question 3

How to determine the binary code of a negative integer?

Answer 3

In order to determine the binary code of a negative integer in the two’s complement system you first need to take the one’s complement by inverting all the bits, and then add 1 to the result.

Question 4

Example of using two’s compliment to convert 85₁₀ to -85₁₀ ?

Answer 4

Example: with 8 bits the decimal number 8510 = 0101 0101₂

The one’s complement is therefore 10101010₂, and the two’s complement, and thus -8510 = 1010 1011₂.

Question 5

How are binary numbers coded with the BCD system?

Answer 5

Example: The code 1001 0001 can be used to represent 91. 8 bits can span the range between 0-99.