Question

2) Show 4 digits to the right of the radix point.

a) Convert 94.87₁₀ to binary. Show your work.

b) Convert 101101.111 to decimal. Show your work.

Answer 1

a)
Converting 94.87 to binary
Convert decimal part first, then the fractional part
> First convert 94 to binary
Divide 94 successively by 2 until the quotient is 0
   > 94/2 = 47, remainder is 0
   > 47/2 = 23, remainder is 1
   > 23/2 = 11, remainder is 1
   > 11/2 = 5, remainder is 1
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1011110
So, 94 of decimal is 1011110 in binary
> Now, Convert 0.87000000 to binary
   > Multiply 0.87000000 with 2. Since 1.74000000 is >= 1. then add 1 to result
   > Multiply 0.74000000 with 2. Since 1.48000000 is >= 1. then add 1 to result
   > Multiply 0.48000000 with 2. Since 0.96000000 is < 1. then add 0 to result
   > Multiply 0.96000000 with 2. Since 1.92000000 is >= 1. then add 1 to result
0.87 of decimal is .1101 in binary
so, 94.87 in binary is 01011110.1101
Answer: 1011110.1101

b)
101101.111
=> 1x2^5+0x2^4+1x2^3+1x2^2+0x2^1+1x2^0+1x2^-1+1x2^-2+1x2^-3
=> 1x32+0x16+1x8+1x4+0x2+1x1+1x0.5+1x0.25+1x0.125
=> 32+0+8+4+0+1+0.5+0.25+0.125
=> 45.875
Answer: 45.875