DigitalDigitcuital and analog systemAnalog circuits are those voltage and current varies continuously. They can take infinite values within specified rangeDigital circuit in which the voltage levels finite. Also called switching circuits or logic circuitsAdvantages of digital circuits

1. Easier to design2. Information storage is easy3. Accuracy and precision are greater4. More versatile5. Less affected by noise6. Can be fabricated on IC chips

Hybrid systemBoth analog and digital techniques can be employed in a same system. Such system are called hybrid system

Logic levels and pulse wave formPositive logicIf the high (+5) voltage is used to represent 1 and low(0) voltage is used to represent 0

Negative logic If the high(+5) voltage is used to represent 0 and low (0) voltage is used to represent 1

Normally 0=0V and +5=1VUsually 0 to 0.8V represent logic 0 and 2 to 5 V represent logic 1Rise time The time taken by the pulse to rise from low to high . (10% to 90% of pulse amplitude)Fall time

The time taken by the pulse to go from high to low (90% to 10% of pulse amplitude)Pulse width

Time between the 50% points on the rising and falling edgeDuty cycle= ON time (pulse width)/ time period (ON time + OFF time)Digital IC

Level of integrationSmall scale integration (SSI)….less than 12 gate circuits per chip eg: logic gates and flip flopMedium scale integration(MSI)….. with 12 t0 99 gate circuits per chip eg: encoder, decoder etcLarge scale integration (LSI)….. with 100 t0 9999 gate circuits per chip eg: small memories & small µpsVery large scale integration (VLSI)…. From 10000 to 99999 gate circuits per chip eg: large memories & large µps Ultra large scale integration (ULSI)….over100000 gate circuits per chip eg: very large memories & very large µps

Number system The decimal number system

The decimal system contains 10 symbols 0,1,2,3,4,5,6,7,8,9,there for base or radix is ten. It is a positional weighted system. Each symbol in the number is called digit. Left most digit in any number is called most significant digit(MSD). Which has the greatest positional weight. The right most digit which has the least positional weight is called (LSD).

In general dn,dn-1 dn-2…….. d1 d0.d-1 d-2 ………d-k

Nine’s and Ten’s complimentsThe 9’s compliment of a decimal is obtained by subtracting each digit of that decimal number from 9. The 10’s

compliment is obtained by adding 1 to its 9’s compliment. Eg: find the 9’s & 10’s compliments of 3465Solution: 9 9 9 9-

3 4 6 5 9’s compliment 6 5 3 4+

110’s compliment 6 5 3 5

End around carry : To perform decimal subtraction using 9’s compliment method ,obtain the 9’s compliment of the subtrahend and add it to minuend . If there is carry indicates that the answer is positive. Add the carry to the LSD of the intermediate result. The carry is called end around carry. If there is no carry indicate answer is negative and the intermediate result is its 9’s compliment form. Take the 9’s compliment to get the result. Eg: subtract 745.81 from 436.62 using 9’s compliment eg: 436.62-745.81

9’s compliment of 436.62 is 563.37745.81+ 436.62+563.37 254.18

1 309.18+ 690.19 1 result…. -309.19

309.19To perform decimal subtraction using 10’s compliment method, obtain the 10’s compliment of the subtrahend and add it to minuend . If there is carry indicates that the answer is positive, ignore it. The result itself is the answer. If there is no carry indicate answer is negative and the result is obtained by taking the 10’s compliment and place negative sign in front of the result

Eg: 2928.54-416.73 eg: 416.73-2928.54

2928.54+ 416.73+ 416.73 7071.27

1 2511.81 ignore the carry 7488.81 result =-2511.81Binary number system

It is a positional weighted system. The base or radix is 2. Hence it has two symbols. A binary digit is called bit.