1. MIPS instruction encoding
j 0x400090
“jump” instruction:
Address 0x400090:
Because this address has only 23 bits, we’ll pad the leading bits by three 0’s, making a total of 26 bits
4. The entire bit pattern is
5. Reorganize in group of 4-bits
6. Hex pattern: 0x

2. CSCI206 - Computer Organization & Programming
Signed Integers
zyBook: 5.5

3. How to actually do add or sub?
If the registers r1, r2, hold values 3, -2, how does the operation
add $r3, $r1, $r2
work?
In general, how does compute do
x = 4 + (-3)

4. How are numbers represented?
A 3-bit system would have 8 different values, -4 through 3, how do we operate such that 3 + (-2) == 1?
011 + (???) = 001 -4 -3 -2 -1 1 2 3 ?
000
001
010
011

5. How to represent signed integers
1. Sign Magnitude
The leading bit represents the sign, 0 for positive, 1 for negative, followed by the value (magnitude).
-127 1
-126

6. How to represent signed integers
2. 1’s Complement
The leading bit represents the sign, invert the rest of the bits if a negative value. -0 1 -1

7. How to represent signed integers
3. 2’s Complement
The leading bit represents the sign, invert the rest of the bits if a negative value, and add 1 to the last bit. -1 1 -2 -9

8. How to represent signed integers
4. Biased (excess)
B = 3 p x
000 -3
001 -2
010 -1
011
100 1
101 2
110 3
111 4
B = 127 p x
-127
128
-126
127 9
A bias value, B, is usually chosen to be roughly in the middle of the range. The actual value x of a bit pattern p is x = p - B. Given x, the bit pattern should be p = x + B.

9. Number Encoding Summary
Sign Magnitude first digit is sign (0=positive), remaining digits are magnitude
1’s Complement first digit is sign, remaining bits are magnitude. Negative numbers are stored inverted.
2’s Complement Same as 1’st complement, but negative numbers are inverted + 1.
Biased redefine zero to be in the middle of the range. The distance from the virtual zero is the magnitude.
Stop, do activity