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Right ANSWER is (d) -10

The EXPLANATION is: The first bit is the sign bit whereas the REST of the bits are magnitude bits. So the number is: 01010 =2^3 * 1 + 2^1* 1 =8+2 =10.

But , the sign bit is 1,

Therefore the answer is : (-2)^10.

Right option is (a) 1

The best I can explain: There is only 1 SIGN bit in all the standards. In a 32-bit format, there is 1 sign bit, 8 bits for the EXPONENT and 23 bits for the mantissa.

The CORRECT OPTION is (d) 1111000

Explanation: The SOLUTION is as FOLLOWS :

Correct answer is (d) MULTIPLIER

Easiest EXPLANATION: 111 is called the multiplier.

Whenever a multiplication is performed the second term is called the multiplier whereas the FIRST term is called the MULTIPLICAND.

The correct OPTION is (a) 0

To explain: The binary MULTIPLICATION of any NUMBER with 0 will give the result 0 itself. Any binary number when MULTIPLIED by 0 gives 0 only. e.g. 1101 * 0000 = 0000.

Correct answer is (d) -10

For explanation I would SAY: The first bit is the sign bit whereas the rest of the bits are magnitude bits. So the number is: 01010 =2^3 * 1 + 2^1* 1 =8+2 =10.

But, the sign bit is 1 ,

THEREFORE the answer is : (-2)10.

The CORRECT option is (a) True

The BEST I can explain: The two result OBTAINED is 0 with a carry of 1. This carry is transferred to the next HIGHER column.

The CORRECT choice is (b) UNDERFLOW

Best explanation: It is REFERRED to as underflow. Nan stands for not a NUMBER. The mantissa is the part after the decimal.

The CORRECT ANSWER is (c) IEEE 754

For explanation: Most computers follow the IEEE 754 bit format for floating point ARITHMETIC. IEEE stands for electrical and electronic engineers. It has all the floating point arithmetic specifications.

Right choice is (a) 64-BIT

Easiest explanation: The 64-bit format is referred to as the double precision format. It has 1 SIGN bit, 8 exponent BITS and 23 bits for the mantissa.

The correct answer is (a) B^n –1 – N

Explanation: Complement of a number can be given by the TERM :

C= B^n –1 – N.

Here,

B= base

n= number of digits

N= the number.

Correct OPTION is (b) False

The explanation is: The two main IEEE FORMATS are 16-bit and 32-bit. No format of 4-bit exists. Further, 8-bit format also exists.

In IEEE format, there are certain bits allotted to sign, EXPONENT and MANTISSA.

The correct CHOICE is (B) 1

Easiest explanation: The binary subtraction 0 – 1 gives the result 1. A borrow of 1 is although generated and is removed from the NEXT HIGHER column.

Correct option is (a) 0

To EXPLAIN I would say: The RESULT obtained is 0 with a CARRY of 1. This carry obtained is added to the next higher column. BINARY system can have only two numbers 0 and 1.

Right ANSWER is (B) F8B2

For EXPLANATION: The 16’s complement is obtained by SUBTRACTING 16 from each of the bits of that number.

Here, 16’s complement of 074E will be F8B2.

The correct option is (C) 345

For explanation: To find the 7’s complement of any NUMBER, we SIMPLY SUBTRACT 7 from each of the bits.

Here, 777-432=345. So, the 7’s complement is 345.

Correct OPTION is (a) 1.010

The best I can explain: The 1’s complement of a number is OBTAINED by reversing the bits with value 1 to 0 and the bits with value 0 to 1. Here, 11111111110.101 gets CONVERTED to 000000001.010 in its 1’s complement format.

Right answer is (B) 3421

To explain I would say: 9’s COMPLEMENT is obtained by SUBTRACTING 9 from each bit of the number.

Here, 9999-6578=3421.

Therefore, the 9’s complement is 3421.

The CORRECT CHOICE is (b) 3

For explanation: 10’s complement is obtained by adding 1 to the 9’s complement of a number.

Here, 9’s complement=999-562=436.

Therefore, 10’s complement=436+1=437.

Right answer is (d) 00101

Explanation: The 1’s complement of a number is obtained by converting all the 0 BITS to 1 and all 1’s TO0’s. Here, 11010 GETS converted to 00101.

Right OPTION is (a) 6

The best explanation: After applying the procedure of BOOTH’s Algorithm, the value obtained will be 6. Even THOUGH the result is obtained in its 2’s complement for but then it is reconverted to its NORMALIZED form.Also, the value obtained after decimal multiplication is the same as the value obtained after binary multiplication.

Right option is (a) Store Accumulator

Best explanation: STA is a data transfer INSTRUCTION given whenever a VALUE is to be COPIED on the accumulator. It is used for the FETCH OPERATION.

Right answer is (c) 4

The BEST EXPLANATION: In Booth’s, N denotes the NUMBER of bits that the higher binary number has when multiplication is performed. Here, since there are 4 bits in 1000, the answer is n=4.

Right answer is (d) 00000

Easiest explanation: The correct answer is d because in case of Booth’s ALGORITHM an extra bit is always ADDED to the BINARY numbers.The 4-bit binary numbers BECOME 5-bit numbers after adding the extra bit. Accumulator is always assigned 0 bits of the order of the binary numbers WHOSE multiplication is to be performed.

Right choice is (d) multiplier

Easiest EXPLANATION: It is referred to as the multiplier. Multiplier is denoted by Q in booth’s algorithm. 22 is CALLED the multiplicand. These numbers are first CONVERTED to their binary equivalents and further the MULTIPLICATION is performed.

Correct choice is (b) BINARY numbers

Easiest EXPLANATION: Booth’s Algorithm is APPLIED only on signed and unsigned binary numbers.

Although, the values of other NUMBER SYSTEMS can be converted to binary, and then the multiplication could be performed.

Correct CHOICE is (a) 01000

Easy explanation: >> is the bitwise LEFT SHIFT operator in binary arithmetic.

Applying >>(left-shift) by 3-bits on the number 11001 will RESULT in 3 ZEROES on the right, i.e., 01000.

The correct CHOICE is (c) 01101

The explanation is: RSC stands for Right-Shift CIRCULANT. So, whenever the NUMBERS are shifted to the right an extra 0 bit is added to the LEFT. Here, after the right shift of 11010, the number OBTAINED will be 01101.

The CORRECT option is (a) True

For explanation: The statement is true as an extra bit is added when we MULTIPLY 2 BINARY numbers by using Booth’s.

Let us take an example if we multiply 2* – 3.

The first step is to obtain the binary equivalents.

Hence, 2=10 and -3=01.

Now after adding the extra bit 2=010 and -3=101.

We add 0 in case of positive numbers WHEREAS 1 in negative numbers.

Right answer is (d) 256

Easiest explanation: The TOTAL NUMBER of patterns that can be formed USING n-bits are 2^n. Here, possible patterns are: 2^8=256.

Right option is (b) m=n’+1

Easiest explanation: 2’s COMPLEMENT is simply OBTAINED by addition of 1. So if n is the number and we take the 2’s complement, add 1 to it, we GET the 2’s complement. Therefore, m=n’+1.

Right choice is (d) 32

To EXPLAIN I would say: The single precision format COMPRISES of 32-bits. It has 1 sign bit, 8 bits for exponent and 23 for the mantissa.

The correct answer is (B) MSB

To ELABORATE: The POSITIVE and negative numbers are separated using the MSB. MSB is the Most Significant BIT. MSB is the leftmost bit. e.g. If 1000 is the NUMBER then 1 is the most significant bit.

Right choice is (d) -2^n-1 to +2^n-1-1

To explain I WOULD SAY: 2’s complement is obtained by adding 1 to the 1’s complement. For e.g. 5 :0101 and 1’s complement=1010and2’s complement=1011.

Correct answer is (b) False

Best explanation: Additive INVERSE of a number is the number which GIVES 0 and not 1 when added to the ORIGINAL number. e.g. number=45, additive inverse =-45, after ADDITION they GIVE 0.

The CORRECT choice is (c) SIGN MAGNITUDE

To explain: Sign Magnitude is used for the representation of positive and NEGATIVE numbers. If the LEFTMOST digit is 0, the number is positive. If the leftmost digit is 1, the number is negative.