Question 1

What is the minimum number of bits required to represent - 143₁₀as a signed binary number in 2's- complement form? A) 8 B) 7 C) 10 D) 9

Accepted Answer

To represent -143 in binary, first, convert 143 to binary, which is 10001111. Since it's a negative number and we're using 2's complement, we need an extra bit to indicate the sign (1 for negative, 0 for positive), making it at least 9 bits to represent -143 correctly.

Question 2

In using the 2's- complement system of subtraction, a negative number in the subtrahend would ultimately be changed to:
A) a negative number in true binary form.
B) a positive number in true binary form.

Accepted Answer

In the 2's-complement system, to represent a negative number, you first take the binary representation of its positive counterpart, invert the bits, and then add 1. Therefore, when you start with a negative number in the subtrahend and convert it to 2's complement for subtraction, you're effectively converting it to a positive number in true binary form.

Question 3

If the numbers 8₁₀and 9₁₀are converted to BCD and added, the initial result would be: A) 0100 1000 B) 1000 0100 C) 0010 0001 D) 0001 0001

Accepted Answer

D

Question 4

In the preceding problem, the erroneous answer generated would be corrected by:
A) converting both BCD code groups to straight binary form and subtracting 0110 from the least significant code group.
B) adding 0110 to the least significant code group.
C) adding 0110 to both the most and least significant BCD code groups.
D) adding 0110 to the most significant code group.

Accepted Answer

When dealing with BCD (Binary-Coded Decimal) arithmetic and an erroneous result occurs due to a sum exceeding 9 (a condition not allowed in BCD since each nibble must represent a decimal digit from 0 to 9), the standard correction method is to add 6 (0110 in binary) to the erroneous digit. This adjustment is known as the "end-around carry" or "nibble correction" and is applied to the least significant digit that has exceeded the BCD limit, hence option B is correct.

Question 5

The following is a 2's- complement signed binary number: 100000000. What is its decimal value? A) - 255₁₀ B) - 256₁₀ C) - 128₁₀ D) - 0₁₀

Accepted Answer

In 2's complement, the leftmost bit is the sign bit. Here, it is 1, indicating a negative number. The magnitude is calculated by inverting the bits and adding 1, resulting in -256.

Question 6

Which of the following represents the four possible outcomes when adding two binary numbers?
A) 0 + 0 = 0, 1 + 0 = 01, 1 + 1 = 11, 1 + 1 + 1 = 11
B) 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 01, 1 + 1 + 1 = 11
C) 0 + 0 = 1, 1 + 0 = 1, 1 + 1 = 01, 1 + 1 + 1 = 01
D) 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 10, 1 + 1 + 1 = 11

Accepted Answer

In binary addition: 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 10 (which is 0 with a carry of 1), and 1 + 1 + 1 = 11 (which is 1 with a carry of 1).

Question 7

The 5- bit 2's- complement equivalent of 12₁₀is: A) 01100 B) 11100 C) 00100 D) 10100

Accepted Answer

The answer of The 5- bit 2's- complement equivalent of...

Question 8

The 5- bit 2's- complement of - 12₁₀is: A) 10100 B) 01100 C) 00100 D) 11100

Accepted Answer

The answer of The 5- bit 2's- complement of -...

Question 9

Multiplication of the unsigned numbers 101101₂and 1011₂results in a product of: A) 101101111₂ B) 111101111₂ C) 110101111₂ D) 111111111₂

Accepted Answer

The answer of Multiplication of the unsigned numbers 101101₂and...

Question 10

The MOST commonly used system for representing signed binary numbers is the:
A) sign- magnitude system.
B) 2's- complement system.
C) 10's- complement system.
D) 1's- complement system.

Accepted Answer

The 2's-complement system is the most commonly used system for representing signed binary numbers because it simplifies the design of arithmetic circuits, allowing for easier addition and subtraction operations without having to distinguish between positive and negative numbers explicitly.

Question 11

When performing subtraction by 2's- complement addition:
A) the minuend is left in its original form and the subtrahend is changed to its 2's- complement.
B) the minuend and subtrahend are both left in their original form.
C) the minuend is changed to 2's- complement and the subtrahend are both changed to the 2's- complement.
D) the minuend and subtrahend are both changed to the 2's- complement.

Accepted Answer

In 2's-complement subtraction, the minuend remains in its original form while the subtrahend is converted to its 2's-complement. This process effectively turns subtraction into addition, where adding the 2's-complement of the subtrahend to the minuend yields the desired result.

Question 12

What is the difference between the sign- magnitude and 2's- complement systems of representing signed binary numbers?
A) In the 2's complement system all numbers, regardless of signs, are entered in the2's- complement preceded by a "1" or "0" to denote sign. In the sign- magnitude method, the magnitude bits represent the true binary value and the bit preceding the MSB represents the sign of the following bits.
B) In the signed- magnitude system all numbers, regardless of their sign, are in straight binary format preceded by a "0" or "1" to denote the sign. In the 2's complement system, the negative numbers are entered in the 2's- complement form preceded by a "1" to acknowledge a negative number whereas positive numbers are entered in straight binary format preceded by a "0" to indicate the sign.
C) In the sign- magnitude system all numbers, regardless of their sign, are in the 2's- complement form preceded by a "0" or "1" to indicate their sign. On the other hand, the 2's- complement system requires the sign- magnitude bits be in straight binary format preceded by a "0" or "1" to denote the proper sign.
D) In the 2's- complement system, all positive numbers are entered in the 2's- complement form preceded by "0" to indicate the sign and all negative numbers are entered in straight binary format preceded by a "1" to indicate the sign. The sign- magnitude system requires that positive and negative numbers be entered in straight binary form preceded by a "0" or "1" to indicate the proper sign.

Accepted Answer

In the signed-magnitude system, the first bit indicates the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude of the number in binary. In the 2's complement system, positive numbers are represented as their binary equivalent with a leading 0, while negative numbers are represented by inverting the binary equivalent of their absolute value and adding 1, with a leading 1 indicating a negative number.

Question 13

One advantage of using the 2's- complement system to represent signed numbers is:
A) addition can be accomplished by performing subtraction.
B) division can be accomplished by performing multiplication.
C) multiplication can be accomplished by performing division.
D) subtraction can be accomplished by performing addition.

Accepted Answer

In the 2's-complement system, subtraction can be performed by adding the 2's complement of the number to be subtracted. This simplifies the hardware design for arithmetic operations in computers.

Question 14

The 2's- complement method of subtraction is to be performed on the 2's- complement signed numbers = 43(- )- 47. Select the correct minuend, subtrahend, signed binary difference, and decimal result. A) 00101011 + 11010001 = 11111100 = - 90₁₀ B) 00101011 + 00101111 = 01011010 = - 90₁₀ C) 11010100 + 10101111 = 110000011 = 90₁₀ D) 00101011 + 00101111 = 01011010 = 90₁₀

Accepted Answer

The correct minuend for -43 is 00101011 (the binary representation of 43), and the correct subtrahend for -47 is 00101111 (the 2's complement of 47). Adding these gives 01011010, which is the binary representation of 90, the correct decimal result.

Question 15

What is the decimal value of the 2's- complement signed binary number 110101101? A) +l74₁₀ B) +83₁₀ C) - 83₁₀ D) - 174₁₀

Accepted Answer

The 2's-complement signed binary number 110101101 is negative because the leftmost bit is 1. To find the decimal value, we first invert the bits (1's complement) and then add 1 (2's complement). 110101101 -> 001010010 -> 001010011 = +83

Question 16

When multiplying numbers in the 2's- complement system, the product's sign is:
A) negative if the signs of the multiplier and multiplicand are the same.
B) negative if the multiplier and multiplicand are both positive signs.
C) positive if the signs of the multiplier and the multiplicand are the same.
D) positive if the sign bits of the multiplier and multiplicand are opposite.

Accepted Answer

In the 2's-complement system, the product of two numbers will have a positive sign if the signs of the multiplier and multiplicand are the same, either both positive or both negative. This is because a negative times a negative equals a positive, and a positive times a positive also equals a positive.

Question 17

Which of the following represents the 2's- complement of the binary number 100110110101₂? A) 111001001010 B) 100110110101 C) 011001001011 D) 101100100101

Accepted Answer

The 2's complement of a binary number is found by inverting all the bits and adding 1 to the least significant bit. The given binary number, after removing the placeholders, is 100110110101. Inverting all bits gives 011001001010, and adding 1 gives 011001001011, which matches option C.

Question 18

The 2's- complement system is to be used to add the signed binary numbers 11110010 and 11110011. Determine the sign and decimal value of each of these numbers and their sum.
A) - 113 and - 114, - 227
B) - 14 and - 13, - 27
C) - 11 and - 16, - 27
D) - 27 and - 13, - 40

Accepted Answer

In the 2's-complement system, the leftmost bit indicates the sign (0 for positive, 1 for negative). To find the decimal value of a negative binary number in 2's-complement, invert all bits and add 1. For 11110010, inverting gives 00001101, adding 1 gives 00001110, which is 14 in decimal, so the original is -14. For 11110011, inverting gives 00001100, adding 1 gives 00001101, which is 13 in decimal, so the original is -13. Adding -14 and -13 gives -27.

Question 19

The 1's- complement of the binary number 010110101₂is: A) 011001010 B) 101001000 C) 101001010 D) 101110101

Accepted Answer

The 1's complement of a binary number is obtained by flipping all the bits in the number. For the given binary number 010110101, flipping each bit results in 101001010.

Question 20

A certain register used to store signed binary numbers provides a 16- bit output. Determine the range of register output values and how many different values the register is capable of containing. A) Range: - 32,768₁₀to +32,767 Values: 65,536₁₀ B) Range: - 32,768₁₀to +32,768 Values: 65,535₁₀ C) Range: - 65,536₁₀to +65,536 Values: 131,071₁₀ D) Range: - 65,536₁₀to +65,535 Values: 131,072₁₀

Accepted Answer

A 16-bit signed binary number can represent values from -32,768 to +32,767, totaling 65,536 different values.

Quiz 6: Digital Arithmetic: Operations and Circuits

What is the minimum number of bits required to represent - 143₁₀as a signed binary number in 2's- complement form?

In using the 2's- complement system of subtraction, a negative number in the subtrahend would ultimately be changed to:

If the numbers 8₁₀and 9₁₀are converted to BCD and added, the initial result would be:

In the preceding problem, the erroneous answer generated would be corrected by:

The following is a 2's- complement signed binary number: 100000000. What is its decimal value?

Which of the following represents the four possible outcomes when adding two binary numbers?

The 5- bit 2's- complement equivalent of 12₁₀is:

The 5- bit 2's- complement of - 12₁₀is:

Multiplication of the unsigned numbers 101101₂and 1011₂results in a product of:

The MOST commonly used system for representing signed binary numbers is the:

When performing subtraction by 2's- complement addition:

What is the difference between the sign- magnitude and 2's- complement systems of representing signed binary numbers?

One advantage of using the 2's- complement system to represent signed numbers is:

The 2's- complement method of subtraction is to be performed on the 2's- complement signed numbers = 43(- ) - 47. Select the correct minuend, subtrahend, signed binary difference, and decimal result.

What is the decimal value of the 2's- complement signed binary number 110101101?

When multiplying numbers in the 2's- complement system, the product's sign is:

Which of the following represents the 2's- complement of the binary number 100110110101₂?

The 2's- complement system is to be used to add the signed binary numbers 11110010 and 11110011. Determine the sign and decimal value of each of these numbers and their sum.

The 1's- complement of the binary number 010110101₂is:

A certain register used to store signed binary numbers provides a 16- bit output. Determine the range of register output values and how many different values the register is capable of containing.