Respuesta :
Step-by-step explanation:
a). The decimal numbers is equal to the sum of binary numbers [tex]$(b_n)$[/tex] times their powers of [tex]$ 2(2^n) .$[/tex]
That is,
[tex]$ b_n \times 2^n + b_{n-1} 2^{n-1}+ ..... + b_02^0 $[/tex]
[tex]$\therefore (1110 \ \ 0100 \ \ 0111 \ \ 1010)_2 $[/tex]
= [tex]$ (0 \times 2^0) + (1 \times 2^1) + (0 \times 2^2) + (1 \times 2^3) + (1 \times 2^4) + (1 \times 2^5) + (1 \times 2^6) + ( 0 \times 2^7) + (0 \times 2^8) + (0 \times 2^9) + (1 \times 2^{10} ) $[/tex][tex]$ + (0 \times 2^{11}) + (0 \times 2^{12}) + (1 \times 2^{13}) + (1 \times 2^{14})+ (1 \times 2^{15})$[/tex]
= 58490
b).
The left most bit of the number represents the sign of the number. If bit = 1, the number is negative else if the bit is 0, the number is positive.
All the remaining bits (i.e all the bits except the leftmost bit) represent the magnitude of the number.
Now, X = 1110 0100 0111 1010
left most bit = 1 => number is negative
remaining bits Y = 110 0100 0111 1010
converting Y to decimal => Y = 25722
c).
Check the leftmost bit(lmb) of the number
if leftmost bit is 0 => convert do the binary to decimal conversion
if leftmost bit is 1, follow the following steps
1. Flip the bits (convert the 0's into 1's and the vice versa)
2. convert the new number from binary to decimal.
3. Add a negative sign / multiply by -1
Now, X = 1110 0100 0111 1010
left most bit = 1;
flipping the bits => Y = 0001 1011 1000 0101
converting Y into decimal => Y = 7045
multiplying Y with -1 => Y = -7045
Therefore, one's complement of X to decimal is -7045
Thus, X = -25722 in decimal.
d).
Check the leftmost bit(lmb) of the number
if leftmost bit is 0 => convert do the binary to decimal conversion
if leftmost bit is 1, follow the following steps
1. Flip the bits (convert the 0's into 1's and the vice versa)
2. convert the new number from binary to decimal.
3. Add 1 to the converted number
4. Add a negative sign / multiply by -1
Now, X = 1110 0100 0111 1010
left most bit = 1;
flipping the bits => Y = 0001 1011 1000 0101
converting Y into decimal => Y = 7045
Adding 1 to Y => Y = 7046
multiplying Y with -1 => Y = -7046
Thus, two's complement of X to decimal is -7046
