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snow_lady [41]
3 years ago
10

For each of the following pairs of signed integers (2’s complement), subtract the second from the first. Show the decimal equiva

lents of each operand and the difference, Indicate overflow where appropriate
a) 111010 001111
b) 000100 011000
c) 010001 011010
d) 010000 100100
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
3 0

Answer:

The answers are

a)111010 - 001111 = 101011 = 43

b) 000100 - 011000 = 111111111 (overflow) = -20

c) 010001 - 011010 = 11111111 (overflow) = -9

d) 010000 - 100100 = 1111111 (overflow) = -20

Step-by-step explanation:

a)111010 = 1×2⁵+1×2⁴+1×2³+0×2²+1×2¹+0×2⁰ = 32+16+8+0+2+0= 58

001111 = 0×2⁵+0×2⁴+1×2³+1×2²+1×2¹+1×2⁰ = 8+4+2+1=15

111010 - 001111 = 101011 = 43

b) 000100 = 0×2⁵+0×2⁴+0×2³+1×2²+0×2¹+0×2⁰ = 4

011000 = 0×2⁵+1×2⁴+1×2³+0×2²+0×2¹+0×2⁰  = 24

000100 - 011000 = 1111111111 (overflow), 4 - 24 =-20

c)  010001 = 1×2⁴+1×2⁰ = 17

011010 = 1×2⁴+1×2³+1×2¹ = 26

010001 - 011010 = 11111111 (overflow) 17-26=-9

d) 010000 = 1×2⁴ = 16

100100 = 1×2⁵+1×2² = 36

010000 - 100100 = 1111111 (overflow) 16-36=-20

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