Question

Q1- CLO-1 Cognitive-3 (Application) Do the arithmetic i) +70+80 and ii) -70-80 using 8-bit signed-2 S COM signed numbers and results are stored in 8-bit registers each). It u results are stored in 8-bit registers each). If the results couldn't be accommodated in 8 bits, an overflow would have occurred. III) How could an overflow in hardware (like using which gate/function)? Q2- CLO-2 Cognitive-4 (Analysis)

Solve

Answer 1

similar - implement 5 +70+80 using 8-bit signed - 2's complement. System Sol Ginen Arithematic opera from 470) +(+80) +70 in Signed 8-bit format - 01000110 +80 in Signed 8-bit format - 01010000 1 carries The . +70 0 1000110 +80 o loroooo +150 10010110 Two signed binary numbers +70 & +80 are stored in two 8-656 registers. The range of numbers that each 8 bit register can accommodate is from binary +27 to -198. Since the sum of the two numbers is +150. It exceeds the capacity of the 8-bit register. is) - 70-80 using 8-bit signed a's comp -70 in 8bit signed a's complement form. Take +70 0 1000110 I + Toger-702's complement +70 -70 = is complement of +70 ti 1011100) both po The a negat- been neg Howe as the obtarned Since 8-bits, dis) How An observing carry ou If condition This Tolli 010

rement Similary -80 in 8-bit signed as complement form -80 = 101160oo. carries: 1o -70 101 11010 -80 I 0110000 -150 01101010 tored in gister can The above statements is true if the numbers are both positive or both negative The 8-bit result that should have been positive has a negative sign and the sbit result that should have been negative bas a positive Sign bit. However, the carry out of sign bit position is faken as the sign bit of the result, the 9 bit answer so obtained will be correct. Since the answer cannot be accommodated within 8-bits, we say that an "overflow occurred" #1) How to implement overflow in hardware An overflow condition can be defected by observing the carry into the sigo bit position and the carry out of the sign bit position. If these two carries are not equal, an overflow condition is observed (produced) . This indicated in problem i) & lis) with red

This overflow can be implement in hardware by using exclusive-OR gate, an overflow will be defected when the output of gate is equal to 1 overflow = Cin into sign bit out of sign bit. = Cin 6 Cout at sign bit position. 07