计算机组件和操作代写 Binary Arithmetic代写

ECSE 2610  Homework #2

Computer Components & Operations (CoCO) 

计算机组件和操作代写 Binary ArithmeticProblem 1. (5 points) Determine the logical expression and draw the logic diagram for the carry out output of a full adder.

Binary Arithmetic  计算机组件和操作代写

Problem 1. (5 points) Determine the logical expression and draw the logic diagram for the carry out output of a full adder.

 

 

Problem 2. (6 points) Give the sign-magnitude binary form. Use fewest bits possible to represent decimal numbers

a) +17₁₀ = ______________

b) -17₁₀ = ______________

c) -124₁₀ = ______________

 

 

Problem 3. (9 points) Convert to two’s-complement binary form.

a) +17₁₀  = ______________

b) -17₁₀  = ______________

c) -124₁₀  = ______________

 

 

Problem 4. (10 points) Binary addition and subtraction in 9-bit sign-magnitude form, check for overflow.

(a) 001100101
– 001011111

(b) 001000101
– 001111010

(c) 011010011
+ 111010001

(d) 011110011
+ 011110101

 

 

Problem 5. (15 points) Perform the following additions of 2’s complement numbers, showing all the carries, check for overflow. Verify the addition by converting to decimal.

(a) 001101111
+ 001110110

(b) 110101011
+ 011001101

(c) 011111111
+ 000000001

(d) 101101111
+ 101001110

(e) 011010011
+ 100101110

 

 

Problem 6. (5 points)

a) What is the largest 7-bit sign-magnitude number? _________________________₁₀

b) What is the smallest (i.e., negative) 9-bit sign-magnitude number? ____________₁₀

c) What is the largest 12-bit 2’s complement number? ________________________₁₀

d) What is the smallest 12-bit 2’s complement number? _______________________₁₀

e) At most how many different values can be represented with 12 bits? ___________₁₀

 

 

 

 

Two’s complement arithmetic and binary codes for decimal numbers  计算机组件和操作代写

 

Problem 7. (10 points) Do these calculations in two’s complement with 7 bits. All numbers below are presented in decimal number system.

a) 15 + 11

b) 15 + (–11)

c) 4 – 11

d) (–11) – 29

 

Problem 8. (10 points) Do these calculations in two’s complement using the minimum number of bits to avoid overflow. All numbers below are presented in decimal number system.

a) 3 + (– 7)

b) – 3 + 7

c) 11 + (– 11)

d) 18– (– 3)

 

Problem 9. (15 points) Represent the decimal numbers below in BCD code, 2421 code, and 1-out-of-10 code

a) 39₁₀

b) 178₁₀

 

Problem 10.(15 points) Represent the following decimal numbers in signed binary fixed point two’s complement form, check for overflow.

Use 5 bits for sign and integer part, and 4 bits for fraction part.

a) 6.25 + 11.75

b) 6.25 + (–11.75)

c) –15.125 – 11.75

d) (–11.75) + 15.125

e) 11.75 + 15.125

 

 

 

 

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