Question 1

Use long division to convert each decimal fraction into a binary expansion.
-$\frac { 9 } { 16 }$
A) $0.101 _ { 2 }$
B) $0.1001 _ { 2 }$
C) $0.10001 _ { 2 }$
D) $0.10011 _ { 2 }$
E) None of these

Accepted Answer

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

Question 2

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent.
-$10110101 _ { 2 } *$
A) −75
B) 75
C) −181
D) 181
E) None of these

Accepted Answer

In two's complement notation, the leftmost bit indicates the sign of the number. If the leftmost bit is 1, the number is negative. To find the decimal equivalent of a negative number in two's complement, first invert all the bits and then add 1. For $10110101_2$, inverting all bits gives $01001010_2$, and adding 1 gives $01001011_2$, which is $75_{10}$ in decimal. Since the original number was negative, its decimal equivalent is $-75$.

Question 3

Find the binary equivalent for each of the following decimal numbers.
-18.8125 
A) $1010.1101 _ { 2 }$
B) $1100.1101 _ { 2 }$
C) $10010.1011 _ { 2 }$
D) $10010.11 _ { 2 }$
E) None of these

Accepted Answer

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

Question 4

Find the decimal equivalent for each of the following binary numbers. -111.1101₂ A) 7.78125 B) 7.8125 C) 7.6875 D) 7.40625 E) None of these

Accepted Answer

The binary number 111.1101 can be converted to decimal by calculating the sum of each bit multiplied by 2 raised to the power of its position. The integer part is 1*2^2 + 1*2^1 + 1*2^0 = 4 + 2 + 1 = 7. The fractional part is 1*2^-1 + 1*2^-2 + 0*2^-3 + 1*2^-4 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125. Adding these gives 7.8125.

Question 5

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors.
-$\begin{array} { r } 
1110 _ { 2 } * \
+ 1011 _ { 2 } * \
\hline
\end{array}$

A) (1) $0001 _ { 2 } *$
B) (1) $0101 _ { 2 }$ *
C) (1) $1001 _ { 2 * }$
D) (1) $1101 _ { 2 * }$
E) None of these

Accepted Answer

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

Question 6

Find the binary equivalent for each of the following decimal numbers.
-0.140625 
A) $0.00101 _ { 2 }$
B) $0.001001 _ { 2 }$
C) $0.0010001 _ { 2 }$
D) $0.000101 _ { 2 }$
E) None of these

Accepted Answer

The decimal 0.140625 can be converted to binary by multiplying by 2 and taking the integer part repeatedly: 0.140625 * 2 = 0.28125 (0), 0.28125 * 2 = 0.5625 (0), 0.5625 * 2 = 1.125 (1), 0.125 * 2 = 0.25 (0), 0.25 * 2 = 0.5 (0), 0.5 * 2 = 1.0 (1). Thus, the binary equivalent is 0.001001.

Question 7

Simplify each of the following by using long division.
-$1111010 _ { 2 } \div 10 _ { 2 }$

A) $101101 _ { 2 }$
B) $111101 _ { 2 }$
C) $111100 _ { 2 }$
D) $100101 _ { 2 }$
E) None of these

Accepted Answer

The answer of Simplify each of the following by using...

Question 8

Translate each of the following decimal numbers into two's complement notation.Use an 8-bit representation.
-−112 
A) $10010100 _ { 2 } *$
B) $10010000 _ { 2 } *$
C) $10001000 _ { 2 } *$
D) $10000100 _ { 2 } *$
E) None of these

Accepted Answer

To represent -112 in 8-bit two's complement, first find the binary of 112, which is 01110000. Invert the bits to get 10001111, then add 1 to get 10010000.

Question 9

Exactly how many bytes are in 64 K?
A) 64,000
B) 67,108,864
C) 65,536
D) 512
E) None of these

Accepted Answer

64 K (Kilobytes) means 64 * 1024 bytes, because 1 Kilobyte equals 1024 bytes. Therefore, 64 * 1024 = 65,536 bytes.

Question 10

Translate each of the following decimal numbers into two's complement notation.Use an 8-bit representation.
-41 
A) $101011 _ { 2 } *$
B) $101101 _ { 2 }$ *
C) $110001 _ { 2 } *$
D) $101001 _ { 2 } *$
E) None of these

Accepted Answer

The answer of Translate each of the following decimal numbers...

Question 11

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent.
-$01100110 _ { 2 } ^ { * }$
A) 102
B) −102
C) 154
D) −154
E) None of these

Accepted Answer

In 8-bit two's complement notation, the first bit is the sign bit. Since the first bit is 0, the number is positive. The remaining bits represent the number in binary, which is 102 in decimal.

Question 12

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors.
-$\begin{array}{r}
1000_{2}^{*} \
+0110_{2}^{*} \
\hline
\end{array}$

A) $1001 _ { 2 } *$
B) $1010 _ { 2 }$ *
C) $1110 _ { 2 }$ *
D) $1101 _ { 2 }$ *
E) None of these

Accepted Answer

The sum of 1000 (which is -8 in two's complement) and 0110 (which is 6) is -2, represented as 1110 in 4-bit two's complement. There is no overflow error.

Question 13

Use long division to convert each decimal fraction into a binary expansion.
-$\frac { 3 } { 32 }$
A) $0.0011 _ { 2 }$
B) $0.000011 _ { 2 }$
C) $0.00101 _ { 2 }$
D) $0.00011 _ { 2 }$
E) None of these

Accepted Answer

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

Question 14

Find the decimal equivalent for each of the following binary numbers.
-$\frac { 1101 _ { 2 } } { 10000 _ { 2 } }$

A) 0.75
B) 0.9375
C) 0.8125
D) 0.875
E) None of these

Accepted Answer

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

Question 15

Simplify each of the following by using long division.
-$11000 _ { 2 } \div 11 _ { 2 }$

A) $1010 _ { 2 }$
B) $1000 _ { 2 }$
C) $1100 _ { 2 }$
D) $1001 _ { 2 }$
E) None of these

Accepted Answer

The binary division of $11000_2$ by $11_2$ results in $1000_2$.

Quiz 2: Binary Numbers

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 9 } { 16 }$

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - $10110101 _ { 2 } *$

Find the binary equivalent for each of the following decimal numbers. -18.8125

Find the decimal equivalent for each of the following binary numbers. -111.1101₂

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array} { r } 1110 _ { 2 } * \\+ 1011 _ { 2 } * \\\hline\end{array}$

Find the binary equivalent for each of the following decimal numbers. -0.140625

Simplify each of the following by using long division. - $1111010 _ { 2 } \div 10 _ { 2 }$

Translate each of the following decimal numbers into two's complement notation.Use an 8-bit representation. -−112

Exactly how many bytes are in 64 K?

Translate each of the following decimal numbers into two's complement notation.Use an 8-bit representation. -41

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - $01100110 _ { 2 } ^ { * }$

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - $\begin{array}{r}1000_{2}^{} \\+0110_{2}^{} \\\hline\end{array}$

Use long division to convert each decimal fraction into a binary expansion. - $\frac { 3 } { 32 }$

Find the decimal equivalent for each of the following binary numbers. - $\frac { 1101 _ { 2 } } { 10000 _ { 2 } }$

Simplify each of the following by using long division. - $11000 _ { 2 } \div 11 _ { 2 }$

Quiz 2: Binary Numbers

Use long division to convert each decimal fraction into a binary expansion. - 916\frac { 9 } { 16 }169​

Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent. - 101101012∗10110101 _ { 2 } *101101012​∗

Find the binary equivalent for each of the following decimal numbers. -18.8125

Find the decimal equivalent for each of the following binary numbers. -111.11012

Add the following binary numbers in 4-bit, two's complement notation. Identify any overflow errors. - 11102∗+10112∗\begin{array} { r } 1110 _ { 2 } * \\+ 1011 _ { 2 } * \\\hline\end{array}11102​∗+10112​∗​​