Chapter 2, Problem 20E

a.

Explanation of Solution

1100 + 0011:

• The process of addition can perform on “1” digit at a time from right to left.
• A sum digit and a carry digit are generated at each point.
• It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
• The addition of 4-bit 2’s complement binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “1111”.
• The given binary numbers having the opposite sign.
• If the sign bit is “0” then the number is positive.
• If the sign bit is “1”, the number is negative.
• If the user adds the input binary numbers of different sign, then no overflow occurs in the result.

Justification:

• The sign bit of the binary number “1100” is “1” and it indicates that this number is negative.
• The decimal value for the binary number “1100” is “-4”
• The sign bit of the binary number “0011” is “0” and it indicates that this number is positive...

b.

Explanation of Solution

1100 + 0100:

• The process of addition can perform on “1” digit at a time from right to left.
• A sum digit and a carry digit are generated at each point.
• It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
• The addition of 4-bit 2’s complement binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “0000”.
• The given binary numbers having the opposite sign.
• If the sign bit is “0” then the number is positive.
• If the sign bit is “1”, the number is negative.
• If the user adds the input binary numbers of different sign, then no overflow occurs in the result.

Justification:

• The sign bit of the binary number “1100” is “1” and it indicates that this number is negative.
• The decimal value for the binary number “1100” is “-4”
• The sign bit of the binary number “0100” is “0” and it indicates that this number is positive...

c.

Explanation of Solution

0111 + 0001:

• The process of addition can perform on “1” digit at a time from right to left.
• A sum digit and a carry digit are generated at each point.
• It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
• The addition of 4-bit 2’s complement binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “1000”.
• If the sign bit is “0” then the number is positive.
• If the sign bit is “1”, the number is negative.
• The given binary numbers having the same positive sign.
• If the user adds the input binary numbers with same sign, then overflow occurs in the result.

Justification:

• The sign bit of the binary number “0111” is “0” and it indicates that this number is positive.
• The decimal value for the binary number “0111” is “7”.

$2^3$	$2^2$	$2^1$	$2^0$	Integer
8	4	2	1
0	1	1	1	7

• The sign bit of the binary number “0001” is “0” and it indicates that this number is positive

d.

Explanation of Solution

1000 – 0001:

• The given operation can also be written as “1000+(-0001)”.
• The process of addition can perform on “1” digit at a time from right to left.
• A sum digit and a carry digit are generated at each point.
• It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
• The 2’s complement of “0001” is “1111”.
• The addition of 4-bit 2’s complement binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “0111”.
• The binary numbers used for addition having the same negative sign.
• If the sign bit is “0” then the number is positive.
• If the sign bit is “1”, the number is negative.
• If the user adds the input binary numbers of same sign, then overflow occurs in the result...

e.

Explanation of Solution

0111 + 1001:

• The process of addition can perform on “1” digit at a time from right to left.
• A sum digit and a carry digit are generated at each point.
• It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
• The addition of 4-bit 2’s complement binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “0000”.
• The given binary numbers having the opposite sign.
• If the sign bit is “0” then the number is positive.
• If the sign bit is “1”, the number is negative.
• If the user adds the input binary numbers of different sign, then no overflow occurs in the result...