Homework 3

# 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