Assertion (A) : In logic circuit, positive logic is represented by logic "0" voltage level is lower than logic "1" voltage level. Reason (R) : Excess 3 code is known as self complementary code.
Both (A) and (R) are correct, but (R) is not correct explanation of (A).
Both statements are individually true, but they concern entirely unrelated matters — one is about voltage conventions, the other about a numeric code — so the answer is option 2.
The assertion — positive logic. In positive logic the more positive voltage represents 1 and the less positive represents 0. In 5 V TTL, 0 is nominally 0 V and 1 is nominally 5 V. The convention is arbitrary but must be declared, because negative logic — the more positive level standing for 0 — is equally workable, and the same physical gate performs a different logical function under the two readings. A gate that is AND in positive logic is OR in negative logic, and NAND becomes NOR, by De Morgan's theorem:
\(\overline{A\cdot B}=\overline{A}+\overline{B}\)
This is why data sheets specify the convention rather than leaving it to be assumed.
The reason — excess-3 is self-complementary. Also true. Excess-3 encodes a decimal digit as its BCD value plus 3:
| Decimal | Excess-3 | 9's complement | Its excess-3 |
|---|---|---|---|
| 0 | 0011 | 9 | 1100 |
| 2 | 0101 | 7 | 1010 |
| 4 | 0111 | 5 | 1000 |
In each row the second code is the bitwise complement of the first. So the 9's complement of a digit — the operation needed for subtraction by complement addition — is obtained simply by inverting every bit, which a row of inverters does in no time at all. The offset of 3 is what centres the code so this works, and it also guarantees that no digit is encoded as 0000, so an all-zero word can be distinguished from the digit zero.
The two statements share nothing. A is a statement about voltage levels at the electrical interface; R is a statement about the arithmetic properties of a decimal encoding. Excess-3's self-complementing property holds whatever voltages represent the bits, and the positive-logic convention applies to every code equally. R is true, but it explains nothing about A.
Hence, both are correct, but (R) is not the explanation of (A).
A byte is
Binary addition of 16 and -83 using 2’s compliment results in:
If (211) x= (152) 8, then the value of base x is
A number may be represented in various number systems. Arrange the following number systems in ascending order based on the number of bits needed to represent the same number.
A. Binary
B. Decimal
C. Hexadecimal
D. Octal
Choose the correct answer from the options given below
What is the decimal value for HEX 2A