4 Bit Arithmetic Unit 4X1 Multiplexers, Cheat Sheet of Operating Systems

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Typology: Cheat Sheet

2020/2021

Uploaded on 05/20/2021

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Roll No: 190630107132
What is 4 Bit Arithmetic Circuit?
1. Arithmetic circuits can perform seven different arithmetic
operations using a single composite circuit.
2. It uses a full adder (FA) to perform these operations. A
multiplexer (MUX) is used to provide different inputs to the
circuit in order to obtain different arithmetic operations as
outputs.
3. Consider the following 4-bit Arithmetic circuit with inputs A and
B. It can perform seven different arithmetic operations by varying
the inputs of the multiplexer and the carry (C0).
Components:
1. 4 units of Full Adders.
2. 4 units of 4X1 Multiplexers.
3. 5 units of NOT Gates.
1. Full Adders: -
Full Adder is the adder which adds three inputs and produces two
outputs. A full adder logic is designed in such a manner that can take
eight inputs together to create a byte-wide adder and cascade the
carry bit from one adder to the another.
2. NOT Gate: -
A NOT gate (also often called Inverter) is a logic gate. Each NOT gate
has only one input signal. Logically with NOT gates, the input and the
output swap, so if you input 1 its outputs as 0; likewise, if you input 0
it outputs as 1.
4 Bit Arithmetic Unit
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Roll No: 190630107132

• What is 4 Bit Arithmetic Circuit?

  1. Arithmetic circuits can perform seven different arithmetic operations using a single composite circuit.
  2. It uses a full adder (FA) to perform these operations. A multiplexer (MUX) is used to provide different inputs to the circuit in order to obtain different arithmetic operations as outputs.
  3. Consider the following 4-bit Arithmetic circuit with inputs A and B. It can perform seven different arithmetic operations by varying the inputs of the multiplexer and the carry (C 0 ).
  • Components:
  1. 4 units of Full Adders.
  2. 4 units of 4X1 Multiplexers.
  3. 5 units of NOT Gates.
  4. Full Adders : - Full Adder is the adder which adds three inputs and produces two outputs. A full adder logic is designed in such a manner that can take eight inputs together to create a byte-wide adder and cascade the carry bit from one adder to the another.
  5. NOT Gate: - A NOT gate (also often called Inverter) is a logic gate. Each NOT gate has only one input signal. Logically with NOT gates, the input and the output swap, so if you input 1 its outputs as 0; likewise, if you input 0 it outputs as 1.

4 Bit Arithmetic Unit

3. 4X1 Multiplexers : - A 4 - to-1 multiplexer consists four data input

lines as D0 to D3, two select lines as S0 and S1 and a single output line Y. The select lines S0 and S1 select one of the four input lines to connect the output line.

  • Circuit Connections: -
  1. 4 full-adder circuits that constitute the 4-bit adder and four multiplexers for choosing different operations.
  2. There are two 4-bit inputs A and B The four inputs from A go directly to the X inputs of the binary adder. Each of the four inputs from B is connected to the data inputs of the multiplexers. The multiplexer's data inputs also receive the complement of B.
  3. The other two data inputs are connected to logic-0 and logic-1. Logic-0 is a fixed voltage value (0 volts for TTL integrated circuits) and the logic-1 signal can be generated through an inverter whose input is 0.
  4. The four multiplexers are controlled by two selection inputs, S₁ and So.
  5. The input carry Cin goes to the carry input of the FA in the least significant position. The other carries are connected from one stage to the next.
  6. 4 - bit output Do...D
  • Working When S1 S0 = 00 If Cin = 0 then D = A+B ; ADD e.g 1010 + 0101 = 1111 If Cin = 1 then D = A+B+1 ; ADD With Carry e.g 1010 + 0011 + 1 = 1110 When S1 S0 = 01 If Cin = 0 then D = A+B’ ; subtract with borrow e.g 1010 + (0011)’ = 0110 If Cin = 1 then D = A+B’+1 ; subtract using 2’s comp. e.g 1010 + (0011)’ + 1 = 0111 When S1 S0 = 10 If Cin = 0 then D = A; Transfer A e.g 1010 = 1010 If Cin = 1 then D = A+1; increament A e.g 1010 + 1 = 1011

Note:- This circuit diagram is made up using Logisim Web terminal. And implemented too. https://circuitverse.org/simulator

  • (^) • Circuit

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