The von Neumann Model

1
1
Bits, Data types, and Operations Chapter 2
COMP 2610
Dr. James Money COMP 2610
2
Signed Integers

• Thus, for simplicity of hardware we use the twos
  complement representation
• How do we compute twos complement?
• Write the magnitude of the number in binary
• Compute the ones complement, that is flip the
  bits
• Add one to the result

3
Signed Integers

• How do we reverse twos complement?
• We apply it again!
• That is
• twos complement(twos complement(N)) N

4
Signed Integers

• If the following 6 bits number is in twos
  complement form, what is the number?
• (101001)2
• Compute ones complement (010110)2
• Add one (010111)2 (23)10
• Thus, the number is -23

5
Binary to Decimal Conversion

• We now systematically look at convert from binary
  to decimal for twos complement stored integers
• We assume the binary number is in the form
• M(bn bn-1 b2 b1 b0)2
• where bi is either 0 or 1.

6
Binary to Decimal Conversion

• Consider the leading bit bn. If it is zero, the
  integer is positive or zero. If it is one, the
  integer is negative.
• If bn1, then compute the twos complement of
  bn-1b1b0. Then
• bn-1x2n-1 b2x22 b1x21 b0x20
• is the magnitude of the value
• If the leading bit bn was 1, then add the
  negative sign.

7
Binary to Decimal Conversion

• Convert the following twos complement
  representations to their decimal values
• 1100 0011
• 0011 0110
• 1111 1110

8
Decimal to Binary Conversion

1. Take the magnitude of the decimal number
2. Convert the magnitude of the number to binary
   form
3. If the number is negative, compute the twos
   complement of the number

9
Review of Unsigned Integers

• To convert from positive decimal number M to
  binary
• Set xM, k0
• Compute x2 y R bk
• Set xy, kk1
• Go to 2 if x?0 and repeat
• The bits are the remainders listed right to left
  b3b2b1b0

10
Decimal to Binary Conversion

• Convert the following decimal numbers to their
  twos complement forms for 8 bits
• 45
• -34
• -2
• 0