## A computer stores the floating number in 32 bit where 1 bit for the sign, 8 bits for the exponent having a biased or (+127) and mantissa has a hidden bit. Show how the floating-point value of -14.3125 would be represented in that computer.

### computer science

##### Description

(1)        (a)        Evaluate the following.

. (Show your workings in octal)

[3 marks]

(b)Convert the answer in part (a) to binary.

[2 marks]

(2)        A computer stores the floating number in 32 bit where 1 bit for the sign, 8 bits for the exponent having a biased or (+127) and mantissa has a hidden bit. Show how the floating-point value of -14.3125 would be represented in that computer.

[6 marks]

(3)        Perform the following calculation in BCD8421. Convert your answer to denary.

3428 - 1089

(Note: Perform the subtraction by using 10’s complement)

[5 marks]

(4)        A = 5.6 is corrected to 1 decimal place and B = 2.65 is corrected to 3 significant figures. Calculate the absolute error and percentage relative error for A2 - 3B.

[9 marks]

(5)        A group of five applicants for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer’s selection, A denote the subset of outcomes corresponding to the selection of two men and B denote the subset corresponding to the selection of at least one woman.

Note: Denote the different men and women by M1, M2 & M3 and W1 & W2 respectively.

List the outcomes in

(a)        S, A & B

[4 marks]

(b)

[1 mark]

(c)

[2 marks]

(d)

[1 mark]

(6)        A sample space contains 5 elements E1, E2, E3, E4 and E5.

(a)       If  , , and . Find the probabilities of E4 and E5.

[4 marks]

(b)       If , find the probabilities of the remaining sample events if you know that the remaining samples are equally likely.

[4 marks]

(7)        A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?

[4 marks]

(8)        20 buses are running between places Kuala Lumpur and Seremban. In how many ways can a person go from Kuala Lumpur to Seremban and return by a different bus?

( Dhaundiyal & Coughlan , 2016)[2 marks]