UNIT 3 COMBINATIONAL LOGIC
Introduction to combinational circuits:
A combinational circuit is the digital logic circuit in which the output depends on the
combination of inputs at that point of time with total disregard to the past state of the
inputs. The digital logic gate is the
building block of combinational circuits. The function implemented by combinational
circuit is depend upon the Boolean expressions. On the other hand, sequential logic
circuits, consists of both logic gates and memory elements such as flip-flops. Figure
below shows the combinational circuit having n inputs and and m outputs. The n
number of inputs shows that there are 2^n possible combinations of bits at the input.
Therefore, the output is expressed in terms m Boolean expressions.
Analysis Procedure
To obtain the output Boolean functions from a logic diagram, proceed as
follows:
1. Label all gate outputs that are a function of input variables with arbitrary
symbols. Determine the Boolean functions for each gate output.
2. Label the gates that are a function of input variables and previously labeled
gates with other arbitrary symbols. Find the Boolean functions for these
gates.
3. Repeat the process outlined in step 2 until the outputs of the circuit are
obtained.
4. By repeated substitution of previously defined functions, obtain the output
Boolean functions in terms of input variables.
Example:
F2 = AB + AC + BC; T1 = A + B + C; T2 = ABC; T3 = F2’T1;
F 1 = T3 + T 2
, F1 = T3 + T2 = F2’T1 + ABC = A’BC’ + A’B’C + AB’C’ + ABC
Derive truth table from logic diagram :
We can derive the truth table in Table 4-1 by using the circuit of Fig.4-2.
Design procedure :
1. Table4-2 is a Code-Conversion example, first, we can list the relation of the
BCD and Excess-3 codes in the truth table.
, Karnaugh map:
For each symbol of the Excess-3 code, we use 1’s to draw the map
for simplifying Boolean function :
Circuit implementation:
z = D’; y = CD + C’D’ = CD + (C + D)’
Introduction to combinational circuits:
A combinational circuit is the digital logic circuit in which the output depends on the
combination of inputs at that point of time with total disregard to the past state of the
inputs. The digital logic gate is the
building block of combinational circuits. The function implemented by combinational
circuit is depend upon the Boolean expressions. On the other hand, sequential logic
circuits, consists of both logic gates and memory elements such as flip-flops. Figure
below shows the combinational circuit having n inputs and and m outputs. The n
number of inputs shows that there are 2^n possible combinations of bits at the input.
Therefore, the output is expressed in terms m Boolean expressions.
Analysis Procedure
To obtain the output Boolean functions from a logic diagram, proceed as
follows:
1. Label all gate outputs that are a function of input variables with arbitrary
symbols. Determine the Boolean functions for each gate output.
2. Label the gates that are a function of input variables and previously labeled
gates with other arbitrary symbols. Find the Boolean functions for these
gates.
3. Repeat the process outlined in step 2 until the outputs of the circuit are
obtained.
4. By repeated substitution of previously defined functions, obtain the output
Boolean functions in terms of input variables.
Example:
F2 = AB + AC + BC; T1 = A + B + C; T2 = ABC; T3 = F2’T1;
F 1 = T3 + T 2
, F1 = T3 + T2 = F2’T1 + ABC = A’BC’ + A’B’C + AB’C’ + ABC
Derive truth table from logic diagram :
We can derive the truth table in Table 4-1 by using the circuit of Fig.4-2.
Design procedure :
1. Table4-2 is a Code-Conversion example, first, we can list the relation of the
BCD and Excess-3 codes in the truth table.
, Karnaugh map:
For each symbol of the Excess-3 code, we use 1’s to draw the map
for simplifying Boolean function :
Circuit implementation:
z = D’; y = CD + C’D’ = CD + (C + D)’
