Digital Logic · Unit 4 · 5 hrs
Combinational Logic
Exam-focused notes for Combinational Logic (Digital Logic, CSC116): what the TU syllabus asks and how it has actually been tested, with 12 solved past questions from this unit.
What this unit covers
- Design Procedure
- Adders
- Subtractors
- Code Conversions
- Analysis Procedure
- Multilevel NAND and NOR Circuits
- Exclusive-OR Circuits
Design Procedure
Explain design procedure of combinational circuits. Design a combinational circuit with three inputs x, y, and z, and three outputs, A, B, and C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input.[10]
1. Problem statement: Understand and state the requirement clearly. 2. Determine input/output variables: Assign symbols and decide the number of input/output lines. 3. Derive the truth table: List all $2^n$ input combinations with corresponding outputs. 4. ...
Full solved answer →What is combinational circuit? Design a combinational circuit with four inputs lines that represent a decimal digit in BCD and four output lines that generate the 1's complement of the input binary patterns.[10]
- Number of input lines: 4 (call them $A, B, C, D$) - Inputs represent a decimal digit in BCD (valid range: 0 to 9) - Number of output lines: 4 (call them $W, X, Y, Z$) - Required output: 1's complement of the input binary pattern No numeric constants missi...
Full solved answer →Design a combinational circuit with three inputs and one output. The output is 1 when the binary value of the inputs is an even number. [5]
- Number of inputs: 3 (let them be $A$ = MSB, $B$, $C$ = LSB) - Number of outputs: 1 (call it $F$) - Condition: $F = 1$ when the binary value of inputs is an even number No missing data. The problem is fully specified. --- Three input bits represent decimal...
Full solved answer →Design a combinational circuit with three inputs and one output. The output is 1 when the binary value of the inputs is an odd number. [5]
- Number of inputs: 3 (call them $A, B, C$) - Number of outputs: 1 (call it $F$) - Condition: $F = 1$ when the binary value of $ABC$ is an odd number All required data is present. --- Let: - $A$ = MSB (weight 4) - $B$ = middle bit (weight 2) - $C$ = LSB (we...
Full solved answer →Design a combinatorial circuit that generates 9's complement of a BCD number.[10]
The 9's complement of a BCD digit N is defined as: 9's complement = 9 - N Since BCD uses 4 bits to represent digits 0 through 9, we need a combinational circuit with 4 inputs (A, B, C, D) and 4 outputs (W, X, Y, Z). --- The BCD input represents digits 0-9. ...
Full solved answer →Design 4-bit even parity generator. [5]
A parity generator is a combinational circuit that generates a parity bit to be appended to a message before transmission. For even parity: the parity bit P is chosen such that the total number of 1s in all bits (message + parity bit) is even. --- Let the 4...
Full solved answer →Design a combinational circuit with three inputs, x, y and z, and three outputs, A, B and C. When the binary input is 0,1,2, or 3, the binary output is one greater than the input. When the binary input is 4,5,6 or 7, the binary output is one less than the input. [5]
- Inputs: $x, y, z$ (3-bit, $x$ = MSB), range 0 to 7 - Outputs: $A, B, C$ ($A$ = MSB) - Rule: - Input in $\{0,1,2,3\}$ → output = input + 1 - Input in $\{4,5,6,7\}$ → output = input − 1 Dec x y z Out(dec) A B C --------------------------------- 0 0 0 0 1 0 ...
Full solved answer →Subtractors
Design a full subtractor with necessary tables and logic diagram. [5]
A full subtractor is a combinational circuit that performs subtraction of three bits: the minuend (A), the subtrahend (B), and the borrow-in (Bin) from the previous stage. It produces two outputs: the difference (D) and the borrow-out (Bout). --- Symbol Mea...
Full solved answer →Design a full subtractor circuit with three inputs $x$, $y$, $B_{in}$ and two outputs $Diff$ and $B_{out}$. The circuit subtracts $x - y - B_{in}$, where $B_{in}$ is the input borrow, $B_{out}$ is the output borrow, and $Diff$ is the difference [5]
A full subtractor is a combinational circuit that performs subtraction of three bits: minuend (x), subtrahend (y), and input borrow (Bin). It produces two outputs: Diff (difference) and Bout (output borrow). The operation performed is: x - y - Bin --- x y B...
Full solved answer →Adders
Derive the Boolean expression for sum and carry of half adder. Draw its combinational circuit. Implement it using only NOR gates. [5]
- Inputs: two single-bit binary values, $A$ and $B$ - Outputs: Sum $S$, Carry $C$ - Constraint: implement using only NOR gates All required information is present in the question. --- A B Sum (S) Carry (C) -------------------------- 0 0 0 0 0 1 1 0 1 0 1 0 ...
Full solved answer →Derive the Boolean expression for sum and carry of half adder. Draw its combinational circuit. Implement it using only NAND gates. [5]
- Inputs: two single bits $A$, $B$ - Outputs: $S$ (Sum), $C$ (Carry) - Constraint for last part: implement using only NAND gates No numeric data missing; this is a derivation/design problem. --- A B Sum (S) Carry (C) -------------------------- 0 0 0 0 0 1 1...
Full solved answer →Exclusive-OR Circuits
Write short notes on (any two): a. SIMM b.RTL c.Parity Checker [5]
--- SIMM stands for Single Inline Memory Module. It is a type of memory module used to add RAM (Random Access Memory) to a computer system. Key Points: - A SIMM is a small circuit board that holds several RAM chips and connects to the motherboard through an...
Full solved answer →Make Unit 4 stick
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