# 1

a) 16#123: 0b000100100011
b) 10#123: 1111011

# 2

a) 11011 = -00101 = -5
b) 1110111 = -0001001 = -9
c) 1010101 = -0101011 = -43
d) 1000000001 = -0111111111 = -255
e) 1111111111 = -0000000001 = -1

# 3
a) -31 = -011111 = ~011110 = 100001
b) -32 = -0100000 = ~0011111 = 1100000
c) -127 = -0111111 = ~01111110 = 10000001
d) -128 = -010000000 = ~001111111 = 110000000
e) -77 = -01001101 = ~01001100 = 10110011
f) -22 = -010110 = ~010101 = 101010

# 4

a) 101 + 011 = 1000
b) 111 + 111 = 1110
c) 1010 + 1010 = 10100
d) 11101 + 1010 = 100111
e) 11111 + 11111 = 111110

# 5

a) 110 - 10 = 100
b) 101 - 11 = 010
c) 1001 - 11 = 110

# 8

f) xy + xy' = x * (y + y') = x * 1 = x
g) (x + y) * (x + y')