Question

Assume 151 and 214 are signed 8-bit decimal integers stored intwo’s complement format. Calculate 151 214 using saturating arithmetic. Th eresult should be written in decimal. Show your work.

Answer 1

In a signed 8-bit two's complement system with saturating arithmetic, adding 151 and 214 exceeds the representable range, thus saturating at the maximum value of 127.

Step-by-step explanation:

The problem asks to calculate the sum of 151 and 214 using saturating arithmetic in a signed 8-bit two's complement format. In this format, the range of representable numbers is from -128 to 127. Firstly, if we naively add 151 and 214, the result is 365. However, since this exceeds the maximum value of 127 that can be represented in this format, the operation saturates and gives the maximum value instead.

Therefore, the result of adding 151 and 214 using saturating arithmetic in an 8-bit signed two's complement system is 127.

Answer 2

The result is -63

Step-by-step explanation:

First, we discover the Binary value of 151 which is 10010111.

1 = most significant bit and it represents the sign as negative.

Two's compliment of 10010111, is calculated by adding 1 to one's compliment. We get 01101001 which is 105 in decimal.

Therefore the value of A (the first part) is -105.

Second, the binary value of 214 = 11010110.

1 = most significant bit and it represents the sign as negative.

Two's compliment of 11010110, is calculated by adding 1 to one's compliment. We get 00101010 which is 42 in decimal.

Therefore, the value of B (the second part) is -42.

Simplify further,

A - B = -105 - (-42)

= -105 + 42

= -63

Therefore, the result is -63,