Question

1. X=01110 and Y=11001 are two 5 bit numbers represented in 2’s complement format. Find the sum of X and Y in 2’s complement form in 8-bit representation. 

2. a. Define self-complementing code with example. 

b. Subtract by using BCD code 357-298 

3. a. Design X-OR gate using minimum number NAND gates. b. Explain how X-NOR gate acting as buffer and inverter. 

Answer 1

1. The given two five bits numbers in 2's formats are given below

$X=01110$

$Y=11001$

So, $X+Y=00111$ by ignoring carry in the 2's

2

The binary coded decimal code in which the combination for the complement of a digit is the complement of the combination for that digit.

The 2421, the excess‐3 and the 84-2-1 codes are examples of self‐complementing codes.

Subtract using BCD:

357-298

The binary representation of the decimal is

357=101100101

298 = 100101010

9's complement of 298

$999-298 =701$

10's complement of 298 is =701+1 = 702

Now, adding 357 and 702 by using BCD addition,

BCD code for 357 : 001101010111

BCD code of 702 : 011100000010

after addition : 101001011001

If BCD is invalid then add 6 : 0110

After addition : 1000001011001

Hence 10 5 9

If we are ignoring left most value then the correct answer will be 59.