Assignment

1. Convert the following decimal numbers to binary, show work

a) 24₁₀
b) 30₁₀
c) 11₁₀
d) 518₁₀

2. Convert the following binary numbers to decimal, show work

a) 110101₂
b) 11011₂
c) 101010.1111₂

3. Convert the following, show work:

a) Decimal 225.5 to binary, octal, and hexadecimal
b) Binary 110.110 to decimal, octal, and hexadecimal
c) Octal 620.77 to decimal, binary, and hexadecimal
d) Hexadecimal 2AD5.D to decimal, octal, and binary

4. Use 1's complement to compute the following subtractions in parts (a) and (b), show work:

a) 1010101 - 1000101
b) 1000101 - 1010101
c) Use 2's complement to compute the same subtractions in parts (a) and (b), show work:

5. An engineer proposed the following logic circuit. Why was the boss very disappointed? Explain and show all work.

6. You are given four signed integers in different number bases

A = +(7A)₁₆ B = -(25)₈ C = (104)₁₀ D = +(11010)₂

a) What is the value n, the smallest number of bits needed to represent all of these numbers in 2's complement representation? What is the largest and smallest number that can be represented?

b) Give the n-bit representations of the four numbers in the 2's complement system, where n is the value determined in (a).

c) Compute using 2's complement arithmetic C + D. Is this the answer you would expect? Explain.