Number Systems

Tom Kelliher, CS 220

Sept. 5, 2003

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Assignment

Read 1.3 of Mano.

Outline

1. Number systems: decimal, binary, hexadecimal.

2. Number ranges.

Coming Up

Base conversion and character representation.

Number Systems

Positional, weighted number systems. Example of a non-weighted number system: Roman numerals. Example of non-positional non-weighted number system: unary.

Radix, digit set.

Decimal Numbers

1. Radix 10, digit set 0--9.

2. .

   Radix point.

3. General case:

   We can substitute any radix and digit set we want.

Binary Numbers

1. Radix 2, digit set: 0, 1.

2. Decimal values of , , and ?

   Binary point

3. Powers of two. K, M, and G.

Hexadecimal Numbers

(Octal is similar --- study on your own.)

1. Radix 16, digit set: 0--9, A--F.

2. Generally used as compact binary form.

   How? --- Powers of two.

3. C Constants: 0XFE23, 0x89ab. (0567).

4. Relationship to binary and decimal.

   

   .

Number Ranges

1. Range of values which can be represented.

   Meaning of unsigned.

2. Consider an n-bit number. How many values can be represented? What is the range of values for an n-bit unsigned number?

3. What is the range of values of an 8-bit unsigned number?

Exercises

Convert the following binary numbers to hexadecimal and decimal:

1. 11100111

2. 00111010

3. 11000111

4. 00011111

5. 11101110