Question

10. Convert 101 1010 (seven bits) into a signed decimal (show work)

15. Give the value of 011 1101 and C=0 with ROL (seven bits, show work)

16. Give the signed decimal value of 93A (12 bits, show work)

18. Give the binary equivalent of the decimal number of 13.57 (assume fixed point, no more than 6 bits left and right of the decimal point)

Answer 1

10)
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   1011010 is flipped to 0100101
II. Add 1 to above result
0100101 + 1 = 0100110
III. Now convert this result to decimal value
Converting 100110 to decimal
100110
=> 1x2^5+0x2^4+0x2^3+1x2^2+1x2^1+0x2^0
=> 1x32+0x16+0x8+1x4+1x2+0x1
=> 32+0+0+4+2+0
=> 38
Answer: -38

15)
011 1101 ROL rotates left and gives 111 1010 and C will be 0

16)
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting 93A to binary
9 => 1001
3 => 0011
A => 1010
So, in binary 93A is 100100111010

Now converting 93A to decimal
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   100100111010 is flipped to 011011000101
II. Add 1 to above result
011011000101 + 1 = 011011000110
III. Now convert this result to decimal value
Converting 11011000110 to decimal
11011000110
=> 1x2^10+1x2^9+0x2^8+1x2^7+1x2^6+0x2^5+0x2^4+0x2^3+1x2^2+1x2^1+0x2^0
=> 1x1024+1x512+0x256+1x128+1x64+0x32+0x16+0x8+1x4+1x2+0x1
=> 1024+512+0+128+64+0+0+0+4+2+0
=> 1734
Answer: -1734

18)
Converting 13.57 to binary
Convert decimal part first, then the fractional part
> First convert 13 to binary
Divide 13 successively by 2 until the quotient is 0
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101
So, 13 of decimal is 1101 in binary
> Now, Convert 0.57000000 to binary
   > Multiply 0.57000000 with 2. Since 1.14000000 is >= 1. then add 1 to result
   > Multiply 0.14000000 with 2. Since 0.28000000 is < 1. then add 0 to result
   > Multiply 0.28000000 with 2. Since 0.56000000 is < 1. then add 0 to result
   > Multiply 0.56000000 with 2. Since 1.12000000 is >= 1. then add 1 to result
   > Multiply 0.12000000 with 2. Since 0.24000000 is < 1. then add 0 to result
   > Multiply 0.24000000 with 2. Since 0.48000000 is < 1. then add 0 to result
0.57 of decimal is .100100 in binary
so, 13.57 in binary is 1101.100100
Answer: 1101.100100