Digital Logic Design homework i need help with. Please work out problem i am ver
ID: 2989634 • Letter: D
Question
Digital Logic Design homework i need help with. Please work out problem i am very confused on these conversions.
1. convert the following 4 bit two's complement numbers to 8-bit two's complement numbers.
a) 0111
b) 1001
2. USB 3.0 can send data at 5 Gbits/sec. How many bytes can it send in 1 minute
3. convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Indicate whether or not the sum overflows a 6-bit result.
a) 16 + 9
b) 27 + 31
c) -4 + 19
d) 3 + -32
e) -16 + -9
f) -27 + -31
Explanation / Answer
1.
a) the number is positive as its first digit is zero.
so, 8-bit: 00000111
b) the number is negative as its first digit is one.
so, 8-bit:11111001
2. 5 giga bits in one second.so in one minute, 5*60 = 30 giga bits.
30 giga bits = 30/8 = 3.75 Giga bytes.
Hence,USb transfer 3.5 Gigabytes in one minute.
3. a) 16 = 010000
+ 9 = 001001
=011001 = 25
b) 27 = 011011
+31 = 011111
= 111010
c) -4 = 111100
9 = 001001
= 1000101 <---- exceeded 8 bits
d) 3 = 000011
-32 = 100000
= 100011
e) -16 = 110000
-9 = 110111
= 1100111 <---- exceeded 6 bits
f) -27 = 100101
-31 = 100001
= 1000110 <--- exceeded 6 bits