Flip Flops and Memory

Flip/Flops

This is a simple flip/flop which acts as a latch. It operates through the use of feedback. Basically there are 4 scenarios. If you don't have a signal through either set or reset then whatever state the flip flop was in, it will stay in. If you input something into the reset but not the set the not Q will change. You can envision this as just a separate signal though through only the bottom wire. If you input into set but not reset, then the Q output will change, or the proper signal setting your "memory" bit to one. Which is why it can be called set. Then the Final is if you input a signal through both set and reset which clears all information, putting both states to 0.

S R Q Q̅

0 0 No change

0 1 0 1

1 0 1 0

1 1 0 0

This flip/flop is equivalent to one bit of memory as it is capable of holding a state.

Binary, 2's complement, Hexadecimal-

So since we are capable of storing a bit of memory, we can string them together to form larger sections of memory. We often refer to bytes of memory, which is 8 bits, which represents 256 different states.

2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
0 1 0 0 1 1 0 1 would then = 77

You can then partition the byte into two halves and write the number in hexadecimal 

the high is
0 1 0 0 = 4
the low is
1 1 0 1 = d

Hexadecimal goes as 0 1 2 3 4 5 6 7 8 9 A B C D E F

2's complement is a way of making the operations of addition multiplication and subtraction identical. If we had these 8 bits be positive only we would count through 256 possible numbers from 0-255. Using two's complement we go from 0 -> 127 and then go back down from -128 to -1.