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Digital Systems Concepts and
Terminology
Digital Systems 1 - Tutorial 2 Solutions
1. Number Representations
a) Binary Representation of Decimal 237 : The binary representation of the decimal number 237 is 11101101.
b) Hexadecimal Representation of Decimal 237 : The hexadecimal representation of the decimal number 237 is ED.
c) Gray Code Representation of Decimal 237 : The Gray code representation of the decimal number 237 is 001000111.
d) ASCII Code Representation of Decimal 237 : The ASCII code representation of the decimal number 237 is 10011011.
2. Binary Arithmetic Operations
a) Addition of 159 and 46 in Binary : 159 (in binary) = 10011111001 46 (in binary) = 101110 159 + 46 = 20520 (in binary)
b) Subtraction of 46 from 159 using Two's Complement : 46 (in binary) = 101110 Two's complement of 46 = 10101001 159 - 46 = 11300 (in binary)
c) Multiplication of 159 and 46 in Binary : 159 (in binary) = 10011111001 46 (in binary) = 101110 159 × 46 = 73345100 (in binary)
d) Division of 159 by 46 in Binary : 159 - 46 = 113 (remainder 2080) 113 - 46 = 67 (remainder 2080) 67 - 46 = 21 (remainder 2080) 21 - 46 = - (remainder 2080) The final result is 11 with a remainder of 2080.
e) Addition of 159 and 46 in BCD : 159 (in BCD) = 0001 0101 1001 0001 0000 46 (in BCD) = 0100 0110 0000 0000 0000 159 + 46 = 0010 0000 0101 0001 0000
3. ASCII Representation with Parity Bit
The hexadecimal number 6AF0H must be communicated using ASCII codes with an even MSB parity bit added. The binary codes required are:
0110 1010 1111 0000 0000
4. Timing Diagrams
a) 3-input NAND Gate Output Waveform : The output waveform for the given input waveforms applied to a 3-input NAND gate is: X = 1 when A = 1, B = 1, and C = 1; otherwise, X = 0.
b) 3-input NOR Gate Output Waveform : The output waveform for the given input waveforms applied to a 3-input NOR gate is: X = 0 when A = 1, B = 1, or C = 1; otherwise, X = 1.
5. Digital System Terminology
a) Propagation Delay : Propagation delay is the time it takes for a signal to propagate through a digital circuit, and it is measured in microseconds, nanoseconds, or picoseconds.
b) Noise Margin : Noise margin is the voltage present as electrical noise in the system that can be tolerated.
c) Fan-in : Fan-in is the number of inputs to a logic gate.
d) Fan-out : Fan-out is the number of gates that can be connected to the output of a logic gate without causing the gate to operate outside of normal limits.
e) Power Dissipation : Power dissipation is the value that indicates the power requirements of the integrated circuit (IC), and it is usually in the form of heat energy conducted away from the IC.
f) CMOS : CMOS stands for Complementary Metal-Oxide Semiconductors.
g) ECL : ECL stands for Emitter-coupled logic.
6. Logic Circuit Analysis
a) Truth Table for the Given Circuit : The truth table for the given circuit is as follows:
| A | B | C | X | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 |
b) Truth Table with XOR in Place of OR Gates : The truth table for the circuit with XOR gates in place of OR gates is as follows:
| A | B | C | X | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 |
