Chapter 2, Problem 17E

a.

Explanation of Solution

01 + 1011:

• Express the given numbers with the same number of bits.
• Addition of leading 0’s do not affect the result.
• 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 given 2-bit  binary number “01” is extended to 4-bit binary number as “0001”
• The addition of the binary numbers is as follows,

b.

Explanation of Solution

11 + 01010101:

• Express the given numbers with the same number of bits.
• The sign of the integer is indicated by the Left most Significant Bit (LSB).
• The number is positive if LSB is “0”, and the number is negative if LSB is “1”.
• The binary number “11” is negative and it is extended by leading 1’s.
• The result does not affected by leading 1’s.
• 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”.
• It the user adds “1” and “0”, it generates the sum digit “1” and carry digit “0”...

c.

Explanation of Solution

0101 + 110:

• Express the given numbers with the same number of bits.
• The sign of the integer is indicated by the Left most Significant Bit (LSB).
• The number is positive if LSB is “0”, and the number is negative if LSB is “1”.
• The binary number “110” is negative and it is extended by leading 1’s.
• The result does not affected by leading 1’s.
• 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”.
• It the user adds “1” and “0”, it generates the sum digit “1” and carry digit “0”...

d.

Explanation of Solution

01 + 10:

• The given binary numbers have the same number of bits.
• The sign of the integer is indicated by the Left most Significant Bit (LSB).
• The number is positive if LSB is “0”, and the number is negative if LSB is “1”.
• 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”.
• It the user adds “1” and “0”, it generates the sum digit “1” and carry digit “0”...