Computer Science Illuminated
Computer Science Illuminated
7th Edition
ISBN: 9781284155617
Author: Nell Dale, John Lewis
Publisher: Jones & Bartlett Learning
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Chapter 4, Problem 61E
Program Plan Intro

Circuit:

  • The circuit is known as the combination of gates that is used to achieve a difficult logical operation.
  • It contains two general categories, they are:
    • Combinational circuit
    • Sequential circuit

Expert Solution & Answer
Check Mark

Explanation of Solution

Given circuit diagram:

Computer Science Illuminated, Chapter 4, Problem 61E

Behavior of the circuit:

  • From the circuit diagram:
    • First, the input A is passed to NOT gate to perform the inverse of A and produces the output as A¯.
    • Next, the inputs B and C are passed into XOR gate to perform the XOR operation of the B and C to produce the output as BC.
      • Note: XOR operation - when both the inputs are the same, then the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
    • Finally, the output of NOT gate and output of XOR gate is passed as the input of AND gate.
      • That is, “A¯” and “BC” are passed as input for AND gate and produces the output A¯(BC).

Truth table:

Step 1:

  • The inputs are A, B, and C for the above circuit diagram:
ABCA¯BCA¯(BC)
000   
001   
010   
011   
100   
101   
110   
111   

Step 2:

  • When the inputs are A as 0, B as 0, and C as 0:
ABCA¯BCA¯(BC)
000100
001   
010   
011   
100   
101   
110   
111   
  • First, the input A as 0 is passed to NOT gate to perform the inverse of the A and produces the output as  0 ¯=1.
  • Next, the inputs B as 0 and C as 0 are passed in the XOR gate to perform the XOR operation of 0 and 0, to produce the output as 00 = 0.
    • Note: XOR operation: when both the inputs are the same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “1” and “0” are passed as input to AND gate and produces the output 10 = 0.

Step 3:

  • When the inputs are A as 0, B as 0, and C as 1:
ABCA¯BCA¯(BC)
000100
001111
010   
011   
100   
101   
110   
111   
  • First, the input A as 0 is passed to NOT gate to perform the inverse of the A and produces the output as  0 ¯=1.
  • Next, the inputs B as 0 and C as 1 are passed in the XOR gate to perform the XOR operation of 0 and 1, to produce the output as 01 = 1.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, output of XOR gate will be 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “1” and “1” are passed as input to AND gate and produces the output 11 = 1.

Step 4:

  • When the inputs are A as 0, B as 1, and C as 0:
ABCA¯BCA¯(BC)
000100
001111
010111
011   
100   
101   
110   
111   
  • First, the input A as 0 is passed to NOT gate to perform the inverse of A and produces the output as  0 ¯=1.
  • Next, the inputs B as 1 and C as 0 are passed in the XOR gate to perform the XOR operation of the 1 and 0, to produce the output as 10 = 1.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “1” and “1” are passed as input for AND gate and produces the output 11 = 1.

Step 5:

  • When the inputs are A as 0, B as 1, and C as 1:
ABCA¯BCA¯(BC)
000100
001111
010111
011100
100   
101   
110   
111   
  • First, the input A as 0 is passed to NOT gate to perform the inverse of the A and produces the output as  0 ¯=1.
  • Next, the inputs B as 1 and C as 1 are passed in the XOR gate to perform the XOR operation of the 1 and 1, to produce the output as 11 = 0.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “1” and “0” are passed as input for AND gate and produces the output 10 = 0.

Step 6:

  • When the inputs are A as 1, B as 0, and C as 0:
ABCA¯BCA¯(BC)
000100
001111
010111
011100
100000
101   
110   
111   
  • First, the input A as 1 is passed to NOT gate to perform the inverse of the A and produces the output as  1 ¯=0.
  • Next, the inputs B as 0 and C as 0 are passed in the XOR gate to perform the XOR operation of the 0 and 0, to produce the output as 00 = 0.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “0” and “0” are passed as input for AND gate and produces the output 00 = 0.

Step 7:

  • When the inputs are A as 1, B as 0, and C as 1:
ABCA¯BCA¯(BC)
000100
001111
010111
011100
100000
101010
110   
111   
  • First, the input A as 1 is passed to NOT gate to perform the inverse of the A and produces the output as  1 ¯=0.
  • Next, the inputs B as 0 and C as 1 are passed in the XOR gate to perform the XOR operation of the 0 and 0, to produce the output as 01 = 1.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “0” and “1” are passed as input for AND gate and produces the output 01 = 0.

Step 8:

  • When the inputs are A as 1, B as 1, and C as 0:
ABCA¯BCA¯(BC)
000100
001111
010111
011100
100000
101010
110010
111   
  • First, the input A as 1 is passed to NOT gate to perform the inverse of the A and produces the output as  1 ¯=0.
  • Next, the inputs B as 1 and C as 0 are passed in the XOR gate to perform the XOR operation of the 0 and 0, to produce the output as 10 = 1.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “0” and “1” are passed as input to AND gate and produces the output 01 = 0.

Step 9:

  • When the inputs are A as 1, B as 1, and C as 1:
ABCA¯BCA¯(BC)
000100
001111
010111
011100
100000
101010
110010
111000
  • First, the input A as 1 is passed to NOT gate to perform the inverse of the A and produces the output as  1 ¯=0.
  • Next, the inputs B as 1 and C as 1 are passed in the XOR gate to perform the XOR operation of the 0 and 0, to produce the output as 11 = 0.
    • Note: XOR operation - when both the inputs are same, the output of XOR gate is 0. Otherwise, the output of XOR gate is 1.
  • Finally, the output of NOT gate and output of XOR gate are passed as the input of AND gate.
    • That is, “0” and “0” are passed as input for AND gate and produces the output 00 = 0.

Therefore, Truth table for the given circuit is:

ABCA¯BCA¯(BC)
000100
001111
010111
011100
100000
101010
110010
111000

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