Question

Need some help with my CS homework. 47. Convert the following numbers from decimal to binary: (a) 12.28125 (b) 0.0234375 (c) 0.7 49 (b) With excess 15 representation, what is the range of numbers as written in binary and in decimal for a five-bit cell? 50. Assuming a three-bit exponent field and a four-bit significand, write the bit pattern for the following decimal values: (c) 0.43 (d) 0.1015625

Answer 1

47
Ans:
a) 12.28125
12
6 0
3 0
1 1
  
12 in binary = 1100

0.28125 * 2 = 0.5625 0
0.5623 * 2 = 1.125 1
0.125 * 2 = 0.250 0
0.250 * 2 = 0.500 0
0.500 * 2 = 1.000 1

.28125 in binary = 01001
12.28125 in binary = 1100.01001

b) 0.0234375
0.0234375*2 = 0.046875 0
0.046875*2 = 0.09375 0
0.09375*2 = 0.1875 0
0.1875*2 = 0.375 0
0.375*2 = 0.75 0
0.75*2 = 1.50 1
0.5*2 = 1.00 1

0.0234375 in binary = 0.0000011

c) 0.7
0.7*2 = 1.4 1
0.4*2 = 0.8 0
0.8*2 = 1.6 1
0.6*2 = 1.2 1
0.2*2 = 0.4 0
0.4*2 = 0.8 0
0.8*2 = 1.6 1
it is repeting sequence
so
0.7 in binary = 1011001