Chapter 2, Problem 18E

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,

• Therefore, the resultant binary bit pattern is “1100”...

b.

Explanation of Solution

11 + 01010101:

• Express the given numbers with the same number of bits.
• 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”.
• The given 2-bit  binary number “11” is extended to 8-bit binary number as “00000011”
• The addition of the binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “01011000”...

c.

Explanation of Solution

0101 + 110:

• Express the given numbers with the same number of bits.
• 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”.
• The given 3-bit  binary number “110” is extended to 4-bit binary number as “0110”
• The addition of the binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “1011”...

d.

Explanation of Solution

01 + 10:

• The given binary numbers have the same number of bits.
• 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”.
• The addition of the binary numbers is as follows,

• Therefore, the resultant binary bit pattern is “11”...