CS 111: Introduction to Computer Science

Binary arithmetic

Due on paper 9:50AM Wednesday, October 28.

1. For each of the following positive binary integers, what are the decimal (base ten) and hexadecimal (base sixteen) equivalents?

   • 10011
   • 10010011
   • 1
2. Add 10110 to 1011. Show your work (in particular, show where you get carries, and where you don't). You can check your work by translating the numbers into decimal, but I want to see you do the usual gradeschool addition algorithm in base 2 instead of base ten.

3. The number 1.398 is equal to 1 + 3/10 + 9/100 + 8/1000. If we move to binary, and use a "binary point" instead of a decimal point, what will the following numbers equal? That is, what are the base ten equivalents of the following binary numbers?

   • 0.11
   • 101.101
4. When you multiply a decimal number by 10, you shift the decimal point to the right one place. How can you shift a binary point to the right?
5. Rewrite the following base-ten numbers as 16-bit two's complement integers: -1, 255, -255, and 1500.
6. What does the bit pattern 01000110 represent if you interpret it as an 8-bit two's complement integer? What if you interpret it as a character using ASCII?

7. Some questions about Unicode.

   • What is the Unicode value for the lower-case beta in the Greek alphabet?
   • What character is represented by the Unicode code point 0x2663? (That's hexadecimal 2663, also known as decimal 9827.)
   • Name two languages that you have never heard of before whose alphabets are included in Unicode.
   • What is Tengwar? What is its status with respect to Unicode?