Introduction to Computing $-$ CPIT $201$

Homework $3($Due October $07)$

The result of the $(1001$ XOR $0111)$ AND NOT$(1111$ OR $($NOT $1001))$

$(1$ point$)$

Draw a logic circuit for the following expression and then determine the output if the inputs are

$(A=0110,B=1001,C=0011,D=1111)$

$(2$ points$)$

$(($NOT $($A AND B$)$ XOR C$)$ AND D$)$ XOR $($NOT$(($C AND D$)$ OR B$)$ OR A$)$

What will be the output when the computer performs $2$ bits arithmetic right shift on the

bit pattern $10101110$ which is stored in two's complement format?

$(1$ point$)$

Verify that if you divide the original number in decimal by $2$ twice you get your final

answer in decimal. Show your work?

What will be the output when the computer performs arithmetic left shift operation on

the bit pattern $11100100$ which is stored in two's complement format?

$(1$ point$)$

Verify that if you multiply the original number in decimal by $2$ you get your final answer

in decimal. Show your work?

Define the operator and the mask you would use to unset the five rightmost bits on the

bit pattern $10010100?$

$(1$ point$)$

Two integers A and B are stored in two's complement format. Show how B is subtracted

from $A.,(-53)-(-27)=(-26).$

$(2$ points$)$

Hint: Let $A=(-53)$ and $B=(-27)$ and show how to do $(A-B)$ in two's complement

format. Use $8-$bits to represent each number in binary.

Verify that your final answer in binary is equal to $-26$ in decimal. Show your work?

Two integers A and $B$ are stored in sign$-$and$-$magnitude format. Show how $B$ is

subtracted from $A.(-53)-(-27)=(-26).$

$(2$ points$)$

Hint: Let $A=(-53)$ and $B=(-27)$ and then use the flowchart for sign$-$and$-$magnitude

format. Use $8-$bits to represent each number in binary.

Verify that your final answer in binary is equal to $-26$ in decimal. Show your work?