number system revision

1. DIGITAL LOGIC DESIGN
BY UNSA SHAKIR

2. Definition
 Digital Logic is a term used to denote the
design and analysis of digital systems.
 Digital Logic is the basis of electronic
systems, such as computers and cell
phones. Digital Logic is rooted in binary
code, a series of zeroes and ones.This
system includes logic gates and facilitates
the design of electronic circuits that convey
information in the form of digital bits, Digital
Logic gate functions include and, or and not.
Design of such system is digital logic design

3. Example:

4. Number Systems

8. Conversion Among Bases

9. Example:
123410 = ?16
12510 = ?2
7058 = ?2
10AF16 = ?2
123410 = ?8
10110101112 = ?8
10101110112 = ?16
10768 = ?16
1F0C16 = ?8

10. Exercise

11. Answer

12. Base 10

13. Review – multiplying powers
 For common bases, add powers
ab  ac = ab+c
26  210 = 216 = 65,536
or…
26  210 = 64  210 = 64k

14. Binary Addition
 Two 1-bit values

15. Binary Addition
 Two n-bit values
◦ Add individual bits
◦ Propagate carries
◦ E.g.,
10101 25
+ 11001 + 31
101110 56

16. Multiplication
 Binary, two 1-bit values

17. Multiplication
 Binary, two n-bit values
◦ As with decimal values
◦ E.g.,
1110
x 1011
1110
1110
0000
1110
10011010

18. 1's complement
 The 1's complement of a number is
found by changing all 1's to 0's and all
0's to 1's. This is called as taking
complement or 1's complement.

19. 2's complement
 The 2's complement of binary number
is obtained by adding 1 to the Least
Significant Bit (LSB) of 1's
complement of the number.
 2's complement = 1's complement + 1

21. • Convert decimal 49 to binary
• Convert binary 100101 to decimal
• Convert 10111101.0112 to decimal
• Convert 1910 and 9910 to binary
• Express 37028 in decimal
• Express 1A2F16 in decimal
EXAMPLES:
• Convert 43910 to octal
• Convert 65010 to hexadecimal
• 1111110001011010012 in hexadecimal

22. • 1111110001011010012 in octal-base
• Express 246910 in BCD
• Express the decimal number 39 as an 8-bit
number
• Find the 1’s complement of 10110010
• Find the 2’s complement of 10110010
• Find the 2’s complement of 10010000
• Represent 2510 in 8-bit and then write 1’s
and 2’s complement form

23. Reference book
 Digital Design, 2nd Ed., M. Morris
Mano, Prentice Hall, 1991.