For each of the following pairs of signed integers (2’s complement), subtract the second from the first. Show the decimal equivalents of each operand and the difference, Indicate overflow where appropriate
a) 111010 001111
b) 000100 011000
c) 010001 011010
d) 010000 100100

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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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