2015F001/homework 3

From CDS 130

Jump to: navigation, search

Homework 3


Contents

  1. Binary Division
  2. Binary Division
  3. Binary Division
  4. Sign-and-magnitude
  5. One's complement
  6. Two's complement
  7. Two's Complement
  8. Two's complement
  9. Representing Negative Numbers
  10. Representing Negative Numbers
  11. Suppose signed integers are represented by 9 bits in a computer architecture. Show respectively the range of the integers (in base 10) in the following methods:
  12. Two's complement for subtraction

1. Binary Division

Calculate 11011102 divided 2410 (without using a calculator), and represent the result in binary.

100.102

2. Binary Division

Calculate 11101101112 divided by 25610 (without using a calculator), and represent the result in binary.

11.101101112

3. Binary Division

Divide the following binary number using binary arithmetic

11101011 / 00011011

1000.101101

4. Sign-and-magnitude

Use the sign-and-magnitude method to represent the signed number (-21)10 in 8 bits.

10010101

5. One's complement

Convert One's Complement number 10001111 to base ten.

(112)10

6. Two's complement

For the computer architecture using two's complement to represent negative numbers, what is the minimum number of bits needed to represent (-256)10.

9 bits

7. Two's Complement

Form the negative equivalent of the following 8-bit Two's Complement numbers

  1. 00111101
  2. 00110110

11000011

11001010

8. Two's complement

In 2's complement, the 4-digit hexadecimal number 7010 is ( ? )10.

9. Representing Negative Numbers

For an 8-bit group, work out the representation for − 3710 in

a) Sign & Magnitude
b) One's Complement
c) Two's Complement
d) Excess-127

(10100101)


(011010)


(100101)

(1011010)

10. Representing Negative Numbers

For an 8-bit group, work out the representation for 3910 in

a) Sign & Magnitude
b) One's Complement
c) Two's Complement
d) Excess-127

100111

100111

100111

10100111

11. Suppose signed integers are represented by 9 bits in a computer architecture. Show respectively the range of the integers (in base 10) in the following methods:

a) Sign & Magnitude
b) One's Complement
c) Two's Complement
d) Excess-127

255 to -255

255 to -255

255 to -255

127 to -127

12. Two's complement for subtraction

Using 8-bit binary numbers as an example (e.g., 37 - 85 ), demonstrate how binary subtraction is carried out in two's complement.

make one number its negative equivalent then add the negative number

Personal tools