Part A: Convert to Decimal (base 10)
Convert ( 3B4_{16} ) to decimal (base 10):
[ 3B4_{16} = 3 \times 16^2 + B \times 16^1 + 4 \times 16^0 ]
Where ( B = 11 ):
[ 3 \times 256 + 11 \times 16 + 4 \times 1 = 768 + 176 + 4 = 948 ]
So, ( 3B4_{16} = 948_{10} ).
Part B: Convert to Binary (base 2)
Convert ( 41_{10} ) to binary (base 2):
[ 41_{10} = 101001_{2} ]
Part C: Add the following Binary Numbers
Add the binary numbers and check the work in decimal:
[ \begin{array}{c} 1110_2 \
1000_2 \ \hline 11010_2 \ \end{array} ]
Now, add ( 11011_2 ) and ( 100_2 ):
[ \begin{array}{c} 11011_2 \
100_2 \ \hline 100111_2 \ \end{array} ]
Check in decimal:
[ 1110_2 = 14_{10} ] [ 1000_2 = 8_{10} ] [ 11011_2 = 27_{10} ] [ 100_2 = 4_{10} ]
[ 14 + 8 = 22 ] [ 27 + 4 = 31 ]
So, the final binary sum is ( 100111_2 ) and the decimal check is ( 31 ).
Part D: Convert 64728 to Hexadecimal (Base 16) through Binary (Base 2)
Convert ( 6472_8 ) to binary (base 2):
[ 6_8 = 110_2 ] [ 4_8 = 100_2 ] [ 7_8 = 111_2 ] [ 2_8 = 010_2 ]
So, ( 6472_8 = 110 100 111 010_2 ).
Now, group the binary digits into sets of four (from right to left):
[ 1101 0011 1010_2 ]
Convert each group to hexadecimal:
[ 1101_2 = D_{16} ] [ 0011_2 = 3_{16} ] [ 1010_2 = A_{16} ]
So, ( 6472_8 = D3A_{16} ).
Part E: Add the following Hexadecimal Numbers
Add ( CB82_{16} ) and ( D956_{16} ):
[ \begin{array}{c} CB82_{16} \
D956_{16} \ \hline 1A4D8_{16} \ \end{array} ]
Show all work, including carries:
[ \begin{array}{c} \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rewrite it in proper math terms with proper symbols pls