vu cs201 Mid Term Subjective Solved Past Paper No.2

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AND gates are used to combine multiple signals, if all the signals are TRUE then the output will also be TRUE. If any of the signals are FALSE, then the output will be false. ANDs aren't used as much as NAND gates; NAND gates use less components and have the advantage that they be used as an inverter. (Page 40)

Power Dissipation

Logic Gates and Logic circuits consume varying amount of power during their operation.

Ideally, logic gates and logic circuit should consume minimal power. Advantages of low power consumption are circuits that can be run from batteries instead of mains power supplies. Thus portable devices that run on batteries use Integrated circuits that have low power dissipation. Secondly, low power consumption means less heat is dissipated by the logic devices; this means that logic gates can be tightly packed to reduce the circuit size without having to worry about dissipating the access heat generated by the logic devices.

Microprocessors for example generate considerable heat which has to be dissipated by mounting small fans. Generally, the Power dissipation of TTL devices remains constant throughout their operation. CMOS device on the other hand dissipate varying amount power depending upon the frequency of operation.

Parallel Binary Adders can be implemented by connecting the required number of 1-bit full adders in a configuration represented in figure 14.9. However, there is a practical limitation to the number of 1-bit Full-Adders that can be connected in parallel. In the 4-bit Parallel Adder, the Most significant bit adder which adds bits A3, B3 and the Carry bit C3, cannot proceed until it receives the Carry from the next least significant 1-bit adder which adds bits A2, B2. The A2, B2 bit adder cannot precede unless it receives the carry input C2 from the A1, B1 adder. The A1, B1 adder in tern depends on A0, B0 adder to provide the carry input. Thus the carry has to propagate through each Full-adder before it reaches the last or most significant full adder. (Page 137)

Digital circuits are formed by the combination of Logic Gates. XOR, XNOR, NAND, NOR are combinational function devices. (Page 133)

OR gates are used to combine multiple signals, if any the signals are TRUE then the output will also be TRUE. If all of the signals are FALSE, then the output will be false.

ORs aren't used as much as NOR gates; NOR gates use less components and have the advantage that they be used as an inverter.

The hexadecimal (Hex) numbering system provides even shorter notation than octal. Hexadecimal uses a base of 16. It employs 16 digits: number 0 through 9, and letters A through F, with A through F substituted for numbers 10 to 15, respectively,

Hexadecimal numbers can be expressed as their decimal equivalents by using the sum of weights method, as shown in the following example:

Weight 210
Hex. Number 1B7
7 x 160 = 7 x 1 = 7
11 x 161 = 11x 16 = 176
1 x 162 = 1 x 256 = 256
Sum of products = 43910

Like octal numbers, hexadecimal numbers can easily be converted to binary or vise versa. Conversion is accomplished by writing the 4-bit binary equivalent of the hex digit for each position, as illustrated in the following example:

Hex. Number 1 B 7
Binary number 0001 1011 0111
Hexadecimal Binary Decimal
0 0000 0
1 0001 1
2 0010 2

Sum-of-Weights Method

Sum-of-weights as the name indicates sums the weights of the Binary Digits (bits) of a Binary Number which is to be represented in Decimal. The Sum-of-Weights method can be used to convert a Binary number of any magnitude to its equivalent Decimal representation.

In the Sum-of-Weights method an extended expression is written in terms of the Binary Base Number 2 and the weights of the Binary number to be converted. The weights correspond to each of the binary bits which are multiplied by the corresponding binary value. Binary bits having the value 0 do not contribute any value towards the final sum expression.

The Binary number 101102 is therefore written in the form of an expression having weights 0 1 2 ,2 ,22 ,23 AND 24 corresponding to the bits 0, 1, 1, 0 and 1 respectively.Weights 20AND 23 do not contribute in the final sum as the binary bits corresponding to these weights have the value 0.

Once the Logic circuit design has been entered its operation is verified by using "test vectors. A "test vectorspecifies the inputs and the corresponding outputs. The software simulates the operation of the logic circuit by applying the test vector and checking the outputs. Test vectors are essentially the same as Truth Tables. (Page 204)