The document provides an overview of binary codes and logic gates, focusing on binary-coded decimal (BCD) representation and its applications in digital systems. It explains the fundamentals of binary codes, such as how n-bit binary codes can represent distinct elements, and discusses various logic gates and their functions. Additionally, the document includes examples of BCD representation and emphasizes the differences between decimal and BCD numbers.

1. BINARY CODES
LOGIC GATES
CST161-3 (Basic Knowledge)
D.R.V.L.B Thambawita
August 21, 2017
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

2. BINARY CODES
LOGIC GATES
Table of contents
1 BINARY CODES
Binary-Coded Decimal (BCD)
2 LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

3. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
Digital systems use signals that have two distinct values and
circuit elements that have two stable states.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

4. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
Digital systems use signals that have two distinct values and
circuit elements that have two stable states.
Digital systems represent and manipulate not only binary
numbers, but also many other discrete elements of
information.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

5. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
Digital systems use signals that have two distinct values and
circuit elements that have two stable states.
Digital systems represent and manipulate not only binary
numbers, but also many other discrete elements of
information.
Any discrete element of information that is distinct among a
group of quantities can be represented with a binary code.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

6. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
Digital systems use signals that have two distinct values and
circuit elements that have two stable states.
Digital systems represent and manipulate not only binary
numbers, but also many other discrete elements of
information.
Any discrete element of information that is distinct among a
group of quantities can be represented with a binary code.
An n-bit binary code is a group of n bits that assumes up to
2n distinct combinations of 1’s and 0’s, with each combination
representing one element of the set that is being coded.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

7. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
Digital systems use signals that have two distinct values and
circuit elements that have two stable states.
Digital systems represent and manipulate not only binary
numbers, but also many other discrete elements of
information.
Any discrete element of information that is distinct among a
group of quantities can be represented with a binary code.
An n-bit binary code is a group of n bits that assumes up to
2n distinct combinations of 1’s and 0’s, with each combination
representing one element of the set that is being coded.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

8. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
A set of four elements can be coded with two bits, with each
element assigned one of the following bit combinations: 00,
01, 10, 11.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

9. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
A set of four elements can be coded with two bits, with each
element assigned one of the following bit combinations: 00,
01, 10, 11.
Bit combination of an n-bit code = 0 to 2n − 1.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

10. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
A set of four elements can be coded with two bits, with each
element assigned one of the following bit combinations: 00,
01, 10, 11.
Bit combination of an n-bit code = 0 to 2n − 1.
The code most commonly used for the decimal digits is the
straight binary assignment.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

11. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
A set of four elements can be coded with two bits, with each
element assigned one of the following bit combinations: 00,
01, 10, 11.
Bit combination of an n-bit code = 0 to 2n − 1.
The code most commonly used for the decimal digits is the
straight binary assignment.
This scheme is called binarycoded decimal.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

12. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary codes
A set of four elements can be coded with two bits, with each
element assigned one of the following bit combinations: 00,
01, 10, 11.
Bit combination of an n-bit code = 0 to 2n − 1.
The code most commonly used for the decimal digits is the
straight binary assignment.
This scheme is called binarycoded decimal.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

13. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary Coded Decimal
Example
18510 = 0001 1000 0101BCD = 101110012
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

14. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Binary Coded Decimal
Do you know?
It is important to realize that BCD numbers are decimal
numbers and not binary numbers, although they use bits in
their representation
The only difference between a decimal number and BCD is
that decimals are written with the symbols 0, 1, 2, , 9 and
BCD numbers use the binary code 0000, 0001, 0010, 1001.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

15. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
BCD Addition
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

16. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
BCD Addition
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

17. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Other Decimal Codes
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

18. BINARY CODES
LOGIC GATES
Binary-Coded Decimal (BCD)
Gray Code
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

19. BINARY CODES
LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
LOGIC GATES
Logic gates are simple digital circuits that take one or more
binary inputs and produce a binary output.
The relationship between the inputs and the output can be
described with a truth table or a Boolean equation.
A truth table lists inputs on the left and the corresponding
output on the right. It has one row for each possible
combination of inputs.
A Boolean equation is a mathematical expression using binary
variables.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

20. BINARY CODES
LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
NOT Gate and Buffer
A NOT gate has one input, A, and one output, Y
The other one-input logic gate is called a buffer
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

21. BINARY CODES
LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
AND gate and OR gate
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

22. BINARY CODES
LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
Other Two-Input Gates
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)

23. BINARY CODES
LOGIC GATES
NOT and Buffer
AND and OR
Other Two-Input Gates
XNOR GATE
Do you know?
The two-input XNOR gate is sometimes called an equality gate
because its output is TRUE when the inputs are equal.
D.R.V.L.B Thambawita CST161-3 (Basic Knowledge)