Number System Chapter 3 Subject: Digital System Year: 2009

3 Overview Decimal Numbers Binary Numbers 1's and 2's Complement Signed Numbers

4 Decimal Numbers In the decimal number system each of ten digits, 0 through 9, represents a certain quantity.

5 Binary Numbers The binary number system is another way to represent quantities. It is less complicated than the decimal system because it has only two digits. The decimal system with its ten digits is a base-ten system; the binary system with its two digits is a base-two system. The two binary digits are 1 and 0.

6 Counting in Binary

7 Counting in Binary con’t Example Binary to decimal Conversion

8 Counting in Binary con’t

9 Decimal to Binary Conversion

10 Decimal to Binary Conversion con’t Repeated division-by-2 method

11 1's and 2's Complement The 1’s complement of binary number is found by changing all 1s to 0s and all 0s to 1s.

12 1's and 2's Complement The 2’s complement of binary number is found by adding 1 to the LSB of the 1’s complement 2’s complement = (1’s complement) + 1

13 Signed Numbers A 0 sign bit indicates a positive number, and a 1 sign bit indicates a negative number