Question

Do the following number conversions assuming two's complement representation is used for binary numbers. Douto check your answers becauses mentioned in class.portul credt will not be please digit is wrong in your answer. Do not put any space between ages/bits in your answers a. (113710 - 02 (8-bit binary number) b. (-97)10 - 12 (8-bit binary number) C. (0101 11002 D10 (decimal number) d. (1010 00112 010 (decimal number e. (3C7B)16 12 (16-bit binary number) f. (0100 1011 1000 1110)2-( 016 (4-digit hexadecimal number

Answer 1

$\small \color{blue}Answer:\;\;$

a)  01110001
b)  10011111
c)  92
d)  -93
e)  0011110001111011
f)  4B8E

Explanation:
-------------
a)
113
Since this is a positive number. we can directly convert this into binary
Divide 113 successively by 2 until the quotient is 0
   > 113/2 = 56, remainder is 1
   > 56/2 = 28, remainder is 0
   > 28/2 = 14, remainder is 0
   > 14/2 = 7, remainder is 0
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1110001
So, 113 of decimal is 1110001 in binary
so, 113 in 2's complement binary is 01110001
Answer: 01110001

b)
-97
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 97 successively by 2 until the quotient is 0
   > 97/2 = 48, remainder is 1
   > 48/2 = 24, remainder is 0
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 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 1100001
So, 97 of decimal is 1100001 in binary
So, 97 in normal binary is 01100001
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   01100001 is flipped to 10011110
Step 3:. Add 1 to above result
10011110 + 1 = 10011111
so, -97 in 2's complement binary is 10011111
Answer: 10011111

c)
since left most bit is 0, this number is positive
so, we can directly convert this into a decimal value
Converting 1011100 to decimal
1011100
=> 1x2^6+0x2^5+1x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x64+0x32+1x16+1x8+1x4+0x2+0x1
=> 64+0+16+8+4+0+0
=> 92
Answer: 92

d)
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.
   10100011 is flipped to 01011100
II. Add 1 to above result
01011100 + 1 = 01011101
III. Now convert this result to decimal value
Converting 1011101 to decimal
1011101
=> 1x2^6+0x2^5+1x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 1x64+0x32+1x16+1x8+1x4+0x2+1x1
=> 64+0+16+8+4+0+1
=> 93
Answer: -93

e)
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 3C7B to binary
3 => 0011
C => 1100
7 => 0111
B => 1011
So, in binary 3C7B is 0011110001111011
Answer: 0011110001111011

f)
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 binary to hexadecimal
Converting 0100101110001110 to hexadecimal
0100 => 4
1011 => B
1000 => 8
1110 => E
So, in hexadecimal 0100101110001110 is 0x4B8E
Answer: 0x4B8E

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