Digital Logic: Combinational Circuits

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Questions and Answers

What is the main function of a half-subtractor?

Perform subtraction of two bits

How many inputs does a half-subtractor have?

What are the two outputs of a half-subtractor?

Difference and Borrow

What type of circuit is a half-subtractor?

Combinational circuit Signup and view all the answers

What is the purpose of FA in the binary adder circuit?

Full Adder Signup and view all the answers

How many full adders are used in the binary adder circuit?

4 Signup and view all the answers

What is the function of a full subtractor?

To subtract one binary number from another Signup and view all the answers

What is the purpose of the control signal M in a binary adder/subtractor?

To select between addition and subtraction operations Signup and view all the answers

What is the output of a 2-to-4 line decoder when the input is 10?

Y0 = 0, Y1 = 1, Y2 = 0, Y3 = 0 Signup and view all the answers

What is the function of an n-to-2^n line decoder?

To decode an n-bit binary number into 2^n possible outputs Signup and view all the answers

What is the purpose of the enable control in a decoder?

To enable the decoder circuit Signup and view all the answers

What is the difference between a binary adder and a binary subtractor?

A binary adder performs addition, while a binary subtractor performs subtraction Signup and view all the answers

What is the purpose of the carry-in flag in a binary adder?

To carry over a bit from the previous addition Signup and view all the answers

What is the output of a 3-to-8 line decoder when the input is 110?

Y0 = 0, Y1 = 0, Y2 = 0, Y3 = 0, Y4 = 0, Y5 = 0, Y6 = 0, Y7 = 1 Signup and view all the answers

What is the difference between a decoder and an encoder?

A decoder decodes an n-bit binary number into 2^n possible outputs, while an encoder encodes a single input into an n-bit binary number Signup and view all the answers

What is the purpose of a binary subtractor?

To subtract one binary number from another Signup and view all the answers

What is the characteristic of a combinational circuit?

Output is a function of input only Signup and view all the answers

What is the purpose of a half adder?

To add 1-bit numbers Signup and view all the answers

What is the output of a half adder when the inputs are x = 1 and y = 1?

Sum = 0, Carry = 1 Signup and view all the answers

What is the function of a full adder?

To add 1-bit numbers and a carry Signup and view all the answers

What is the equation for the sum output of a full adder?

S = xy'z' + x'yz' + x'y'z + xyz Signup and view all the answers

What is the equation for the carry output of a full adder?

C = xy + xz + yz Signup and view all the answers

What is the purpose of the HA blocks in a full adder circuit?

To add the two inputs and a carry Signup and view all the answers

How many inputs does a full adder circuit have?

3 Signup and view all the answers

What is the output of a full adder when the inputs are x = 1, y = 1, and z = 1?

Sum = 1, Carry = 1 Signup and view all the answers

What is the purpose of a binary adder?

To add two binary numbers Signup and view all the answers

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Study Notes

Combinational Circuits

Output is a function of input only, with no feedback.
When input changes, output may change after a delay.

Binary Adder

Half Adder:
- Adds 1-bit plus 1-bit.
- Produces Sum and Carry.
- Truth table:
  - x y C S
  - 0 0 0 0
  - 0 1 0 1
  - 1 0 0 1
  - 1 1 1 0
Full Adder:
- Adds 1-bit plus 1-bit plus 1-bit.
- Produces Sum and Carry.
- Truth table:
  - x y z C S
  - 0 0 0 0 0
  - 0 0 1 0 1
  - 0 1 0 0 1
  - 0 1 1 1 0
  - 1 0 0 0 1
  - 1 0 1 1 0
  - 1 1 0 1 0
  - 1 1 1 1 1
- S = xy'z'+x'yz'+x'y'z+xyz = x ⊕ y ⊕ z
- C = xy + xz + yz

Binary Adder Circuit

Full Adder circuit:
- Consists of two half adders and an OR gate.
- Produces Sum and Carry outputs.

Binary Adder with Multiple Bits

Binary Adder with multiple bits:
- Consists of multiple full adders.
- Each full adder adds corresponding bits of two binary numbers.
- Carry output from each full adder is used as input to the next full adder.

Binary Subtractor

Uses 2's complement with binary adder:
- x - y = x + (-y) = x + y' + 1
Binary Subtractor circuit:
- Uses a binary adder with inverters and an OR gate.

Binary Adder/Subtractor

Binary Adder/Subtractor circuit:
- Uses a binary adder with an additional control signal (M).
- M = 0: F = x + y
- M = 1: F = x - y

Decoders

Binary Decoder:
- Extracts "information" from the code.
- Only one output is active (lamp turns on).
2-to-4 Line Decoder:
- Truth table:
  - I1 I0 Y3 Y2 Y1 Y0
  - 0 0 0 0 0 1
  - 0 1 0 0 1 0
  - 1 0 0 1 0 0
  - 1 1 1 0 0 0
3-to-8 Line Decoder:
- Truth table:
  - I2 I1 I0 Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0
  - (all possible combinations of I2, I1, I0)
"Enable" Control:
- Decoder with an enable control signal (E).
- E = 0: all outputs are 0.
- E = 1: Decoder functions normally.