Binary addition and subtraction
- 1. ADDITION & SUBTRACTION Un Signed Arithmetic Signed Arithmetic add addi sub The MIPS recognizes or ignores overflow by two kinds of arithmetic instructions addu addui subu cause exceptions on overflowdo not cause exceptions on overflow
- 2. OVER FLOW? No Over Flow Over Flow Overflow occurs when the result from an operation cannot be represented with the available hardware Operation Operand A Operand B A + B > 0 < 0 A + B < 0 > 0 A – B > 0 > 0 A – B < 0 < 0 Eg: (+10) + (-6) = +4 (-10) + (+6) = -4 Eg: (+10) - (+6) = +4 (-10) - (-6) = -4
- 3. OVER FLOW? Over Flow Overflow occurs when the result from an operation cannot be represented with the available hardware Addition 10000 +10 01010 +6 00110 (+) Over Flow 10111 -5 1011 -4 1100 (+) Over Flow
- 4. OVER FLOW? Over Flow Overflow occurs when the result from an operation cannot be represented with the available hardware Subtraction 11100 +6 00110 -10 10110 (-) Over Flow 0110 -6 1010 +4 0100 (-) Over Flow
- 5. EXAMPLE Assume 185 and 122 are unsigned 8-bit decimal integers. Calculate 185 – 122. Is there over flow, under flow, or neither? 10111001 01111010 (-) 185 122 11 0 1 1 1 010 1 0 110 1 1 110 10 Neither Over Flow nor Under FlowOperation Operand A Operand B A + B > 0 < 0 A + B < 0 > 0 A – B > 0 > 0 A – B < 0 < 0 Computer Organization and Design by David A Patterson – Page no. 237 Condition for No Over Flow
- 6. EXAMPLE Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format. Calculate 185 + 122. Is there over flow, under flow, or neither? 10111001 01111010 +122 (+) 185 122 1100110 Neither Over Flow nor Under Flow -57 1111 10 Operation Operand A Operand B A + B > 0 < 0 A + B < 0 > 0 A – B > 0 > 0 A – B < 0 < 0 Computer Organization and Design by David A Patterson – Page no. 237 Condition for No Over Flow
- 7. EXAMPLE Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format. Calculate 185 - 122. Is there over flow, under flow, or neither? 10111001 01111010 +122 (-) 185 122 1111110 Over Flow -57 0 Computer Organization and Design by David A Patterson – Page no. 237