Question

Q1) Convert the following negative decimal numbers to 8 bit binary using the 2’s complement (show the steps):

a) -39

b) -127

Q2) Solve the following subtraction problems using 2's complement representation. (Show the steps using 8-bits)

a) 19 – 87

b) 89 – 5

Q3) Convert the following numbers into scientific notation: (Note: to show ten raised to the power of n, you can type as 10^n)

a) 654.345

b) 0.000000324235

c) 25600000000000

Q4) Convert the following numbers out of scientific notation:

a) 1.234 X 10^-5

b) 7.345 X 10^10

c) 4.76456E-23

Q5) Convert the following decimal numbers into the IEEE 754 single-precision floating point representation. (Show the steps):

a) -64.1875

Answer 1

Answer 1.a:

39->00100111 (decimal to binary)(The negative sign is ignored in this step)

00100111->11011000 (convert to its 1's complement just by flipping the bits)

11011000+1->11011001 (convert to 2's complement by adding 1 to the 1's complement)

Answer 1.b:

The process remains the same as question 1.a.

127->01111111 (decimal to binary)

01111111->10000000 (convert to its 1's complement just by flipping the bits)

10000000+1->10000001 (convert to 2's complement by adding 1 to the 1's complement)

Binary enavalint 9 00010011 81-7 ฮเ010111 g2. a) 1-87 O0010O11 (/9) -01010111 C81) Take 2's plement og -01 olouI 87) 10101001 02's complonent) Now add 001u I 10101001 10111 100 -68)

Anoe 26) 89-5 -010100 500000101 OiollooI (&a) - Co00O1O(-s) Take 2'semplernen 96-00000101 (- Add 0101100 01010100 be ducaroled . TIL anAweん16 01010100 (84)

hever 3.a) 654 345 654 34s 65.4345 o 6.5434s ((ioxio) 45434/(c) 6 54345x102 Answeん3.6) 0.000000324235 o 00000 03242350.0000032235/io 0.0000 324ssoxo - 0.00032423 Suox loxiD) t o.ooS24235/11ORIOXIOXİo) :0 0324235 Corioxio iox o) 0. 324235/oxioxioxoi0 x1o) #3. 2423s/(cox 10 x 10x10x10x 10x10) 3.24235/Cov 3 24 23s x 107

Answex 3c) 2 5600000000000 256ooooooooooo = 2560000000000 x10 ะ 256000000000 x10x10 25600000000 X 10x10x10 .256000000 x 10x10x10x10 xo XLO : 25600000 x oxoxiox ioxIOxiO 4.56 x o'3

4.764s&e-23 4.76456 x10-23 つ С. 476456 x102- 0.047 64s6 x 10-2' 0-oooooooooooooo ooooooo04764s ニ

234x0123 K10 Ο "Οι 234 x 10-3 0.001239 10-1 τ 0.0001239 x10-1 10 7, 34s x1o'o = 73.45 x109 734,5 x10° 73450 xu0 734500 x lo5 7345000 x 10 τ73ysoooox 103 ะ 734s ooooooo

Stip 1 : 6/t1ET5 → t000000 , 0011 Stip3 : exponent r 127。133 1331000o101 Stap 4. Take de-a@m4%aling point ee 0000000o 7 0ooooooolioooooodoodooo tt mantma and in al onder bunbsny hesult Ilooooto1000000o o1 0000000000000 (31 hit) Answer?> -64. IETS → C 280 6000h.