Question 1

Find the binary equivalent for each of the following decimal numbers.
-125 
A) $1111101 _ { 2 }$
B) $1010100 _ { 2 }$
C) $1101110 _ { 2 }$
D) $1010000 _ { 2 }$
E) None of these

Accepted Answer

125 in decimal is equivalent to $1111101_2$ in binary. This conversion can be done by repeatedly dividing the number by 2 and keeping track of the remainders.

Question 2

Use long division to convert each decimal fraction into a binary expansion.
-$\frac { 5 } { 64 }$

Accepted Answer

The answer of Use long division to convert each decimal...

Question 3

Exactly how many bytes are in 4 GB?

Accepted Answer

The answer of Exactly how many bytes are in 4...

Question 4

Find the decimal equivalent for each of the following binary numbers.
-$10110001 _ { 2 }$
A) 171
B) 173
C) 175
D) 177
E) None of these

Accepted Answer

The answer of Find the decimal equivalent for each of...

Question 5

Add the following binary numbers.
-$\begin{array}{r}
11001110_{2} \
+01100110_{2} \
\hline
\end{array}$

A) $101110100 _ { 2 }$
B) $100110100 _ { 2 }$
C) $100110110 _ { 2 }$
D) $110110100 _ { 2 }$
E) None of these

Accepted Answer

The answer of Add the following binary numbers.
-$\begin{array}{r}
11001110_{2} \
+01100110_{2} \
\hline
\end{array}$

A)...

Question 6

Use long division to convert each decimal fraction into a binary expansion.
-$\frac { 7 } { 8 }$

Accepted Answer

The answer of Use long division to convert each decimal...

Question 7

Add the following binary numbers.
-$\begin{array}{r}
1011_{2} \
+1101_{2} \
\hline
\end{array}$
 
A) $11001 _ { 2 }$
B) $10100 _ { 2 }$
C) $11010 _ { 2 }$
D) $11000 _ { 2 }$
E) None of these

Accepted Answer

The answer of Add the following binary numbers.
-$\begin{array}{r}
1011_{2} \
+1101_{2} \
\hline
\end{array}$
...

Question 8

Find the decimal equivalent for each of the following binary numbers.
-$10001.10001 _ { 2 }$

Accepted Answer

The answer of Find the decimal equivalent for each of...

Question 9

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors.
-$\begin{array} { r } 
1111 _ { 2 } { } ^ { * } \
+ 1101 _ { 2 } ^ { * } \
\hline
\end{array}$

Accepted Answer

The answer of Add the following binary numbers in 4-bit,...

Question 10

Multiply each pair of binary numbers.
-$\begin{array} { r } 
1110 _ { 2 } \
\times \quad 10 _ { 2 } \
\hline
\end{array}$

A) $10101 _ { 2 }$
B) $11000 _ { 2 }$
C) $11100 _ { 2 }$
D) $10100 _ { 2 }$
E) None of these

Accepted Answer

The answer of Multiply each pair of binary numbers.
-\(\begin{array} {...

Question 11

Find the decimal equivalent for each of the following binary numbers.
-$\frac { 10110 _ { 2 } } { 10000000 _ { 2 } }$

Accepted Answer

The answer of Find the decimal equivalent for each of...

Question 12

Find the binary equivalent for each of the following decimal numbers.
-13.00390625

Accepted Answer

The answer of Find the binary equivalent for each of...

Question 13

Find the binary equivalent for each of the following decimal numbers.
-92 
A) $1011110 _ { 2 }$
B) $1011100 _ { 2 }$
C) $1101100 _ { 2 }$
D) $1011101 _ { 2 }$
E) None of these

Accepted Answer

92 in decimal is equal to $1011100 _ { 2 }$ in binary. This can be determined by dividing 92 by 2 repeatedly and noting the remainders.

Question 14

Multiply each pair of binary numbers.
-$\begin{array}{r}
11010_{2} \
\times \quad 101_{2} \
\hline
\end{array}$

A) $10000010 _ { 2 }$
B) $10010010 _ { 2 }$
C) $10001010 _ { 2 }$
D) $10000100 _ { 2 }$
E) None of these

Accepted Answer

The multiplication of binary numbers $11010_2$ and $101_2$ results in $10000010_2$.

Question 15

Perform the following binary subtractions.
-$\begin{array}{r}
1111_{2} \
-1101_{2} \
\hline
\end{array}$

A) $0011 _ { 2 }$
B) $0101 _ { 2 }$
C) $0001 _ { 2 }$
D) $0010 _ { 2 }$
E) None of these

Accepted Answer

Subtracting binary numbers follows the same principles as decimal subtraction, but with base 2. Here, starting from the right: 1 - 1 = 0, 1 - 0 = 1, 1 - 1 = 0, and 1 - 1 = 0, resulting in $0010_{2}$.

Question 16

Find the decimal equivalent for each of the following binary numbers.
-$1110 _ { 2 }$
A) 12
B) 13
C) 14
D) 15
E) None of these

Accepted Answer

The binary number $1110_2$ can be converted to decimal by multiplying each digit by 2 raised to the power of its position, counting from right to left starting at 0. So, $1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 8 + 4 + 2 + 0 = 14$.

Question 17

Find the binary equivalent for each of the following decimal numbers.
-0.6328125

Accepted Answer

The answer of Find the binary equivalent for each of...

Question 18

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors.
-$\begin{array} { r } 
0101 _ { 2* } \
+ 0010 _ { 2* } \
\hline
\end{array}$

Accepted Answer

The answer of Add the following binary numbers in 4-bit,...

Question 19

Perform the following binary subtractions.
-$\begin{array} { r } 
1110 _ { 2 } \
- 0101 _ { 2 } \
\hline
\end{array}$

A) $0001 _ { 2 }$
B) $1001 _ { 2 }$
C) $1011 _ { 2 }$
D) $0011 _ { 2 }$
E) None of these

Accepted Answer

Subtracting binary numbers follows the same principles as decimal subtraction, but with base 2. For $1110_2 - 0101_2$, we subtract each bit from right to left, borrowing as necessary:- $0 - 1$ requires borrowing, turning the $1$ (in the 2's place) into $0$ and the $0$ (in the 1's place) into $2$ (in binary, $10$). So, $10 - 1 = 1$.- $0 - 0 = 0$, but remember we borrowed, so this place is already $0$.- $1 - 1 = 0$.- $1 - 0 = 1$.Thus, the result is $1001_2$.

Question 20

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent.
-$00001111 _ { 2 }$

Accepted Answer

The answer of Each of the following numbers are in...

Quiz 2: Binary Numbers

Find the binary equivalent for each of the following decimal numbers. -125

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 5 } { 64 }$

Exactly how many bytes are in 4 GB?

Find the decimal equivalent for each of the following binary numbers. - $10110001 _ { 2 }$

Add the following binary numbers. - $\begin{array}{r}11001110_{2} \\+01100110_{2} \\\hline\end{array}$

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 7 } { 8 }$

Add the following binary numbers. - $\begin{array}{r}1011_{2} \\+1101_{2} \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $10001.10001 _ { 2 }$

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array} { r } 1111 _ { 2 } { } ^ { * } \\+ 1101 _ { 2 } ^ { * } \\\hline\end{array}$

Multiply each pair of binary numbers. - $\begin{array} { r } 1110 _ { 2 } \\\times \quad 10 _ { 2 } \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $\frac { 10110 _ { 2 } } { 10000000 _ { 2 } }$

Find the binary equivalent for each of the following decimal numbers. -13.00390625

Find the binary equivalent for each of the following decimal numbers. -92

Multiply each pair of binary numbers. - $\begin{array}{r}11010_{2} \\\times \quad 101_{2} \\\hline\end{array}$

Perform the following binary subtractions. - $\begin{array}{r}1111_{2} \\-1101_{2} \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $1110 _ { 2 }$

Find the binary equivalent for each of the following decimal numbers. -0.6328125

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array} { r } 0101 _ { 2* } \\+ 0010 _ { 2* } \\\hline\end{array}$

Perform the following binary subtractions. - $\begin{array} { r } 1110 _ { 2 } \\- 0101 _ { 2 } \\\hline\end{array}$

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - $00001111 _ { 2 }$

Quiz 2: Binary Numbers

Find the binary equivalent for each of the following decimal numbers. -125

Use long division to convert each decimal fraction into a binary expansion. - 564\frac { 5 } { 64 }645​

Exactly how many bytes are in 4 GB?

Find the decimal equivalent for each of the following binary numbers. - 10110001210110001 _ { 2 }101100012​

Add the following binary numbers. - 110011102+011001102\begin{array}{r}11001110_{2} \\+01100110_{2} \\\hline\end{array}110011102​+011001102​​​

Use long division to convert each decimal fraction into a binary expansion. - 78\frac { 7 } { 8 }87​

Add the following binary numbers. - 10112+11012\begin{array}{r}1011_{2} \\+1101_{2} \\\hline\end{array}10112​+11012​​​

Find the decimal equivalent for each of the following binary numbers. - 10001.10001210001.10001 _ { 2 }10001.100012​

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - 11112∗+11012∗\begin{array} { r } 1111 _ { 2 } { } ^ { * } \\+ 1101 _ { 2 } ^ { * } \\\hline\end{array}11112​∗+11012∗​​​

Multiply each pair of binary numbers. - 11102×102\begin{array} { r } 1110 _ { 2 } \\\times \quad 10 _ { 2 } \\\hline\end{array}11102​×102​​​

Find the decimal equivalent for each of the following binary numbers. - 101102100000002\frac { 10110 _ { 2 } } { 10000000 _ { 2 } }100000002​101102​​

Find the binary equivalent for each of the following decimal numbers. -13.00390625

Find the binary equivalent for each of the following decimal numbers. -92

Multiply each pair of binary numbers. - 110102×1012\begin{array}{r}11010_{2} \\\times \quad 101_{2} \\\hline\end{array}110102​×1012​​​

Perform the following binary subtractions. - 11112−11012\begin{array}{r}1111_{2} \\-1101_{2} \\\hline\end{array}11112​−11012​​​

Find the decimal equivalent for each of the following binary numbers. - 111021110 _ { 2 }11102​

Find the binary equivalent for each of the following decimal numbers. -0.6328125

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - 01012∗+00102∗\begin{array} { r } 0101 _ { 2* } \\+ 0010 _ { 2* } \\\hline\end{array}01012∗​+00102∗​​​

Perform the following binary subtractions. - 11102−01012\begin{array} { r } 1110 _ { 2 } \\- 0101 _ { 2 } \\\hline\end{array}11102​−01012​​​

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - 00001111200001111 _ { 2 }000011112​

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 5 } { 64 }$

Find the decimal equivalent for each of the following binary numbers. - $10110001 _ { 2 }$

Add the following binary numbers. - $\begin{array}{r}11001110_{2} \\+01100110_{2} \\\hline\end{array}$

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 7 } { 8 }$

Add the following binary numbers. - $\begin{array}{r}1011_{2} \\+1101_{2} \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $10001.10001 _ { 2 }$

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array} { r } 1111 _ { 2 } { } ^ { * } \\+ 1101 _ { 2 } ^ { * } \\\hline\end{array}$

Multiply each pair of binary numbers. - $\begin{array} { r } 1110 _ { 2 } \\\times \quad 10 _ { 2 } \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $\frac { 10110 _ { 2 } } { 10000000 _ { 2 } }$

Multiply each pair of binary numbers. - $\begin{array}{r}11010_{2} \\\times \quad 101_{2} \\\hline\end{array}$

Perform the following binary subtractions. - $\begin{array}{r}1111_{2} \\-1101_{2} \\\hline\end{array}$

Find the decimal equivalent for each of the following binary numbers. - $1110 _ { 2 }$

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array} { r } 0101 _ { 2* } \\+ 0010 _ { 2* } \\\hline\end{array}$

Perform the following binary subtractions. - $\begin{array} { r } 1110 _ { 2 } \\- 0101 _ { 2 } \\\hline\end{array}$

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - $00001111 _ { 2 }$