Latches

$\bar{S}\bar{R}$ latches

$\bar{S}$ represents “SET” and $\bar{R}$ represents “RESET”

• Recall from Intuition Behind Storing Values, for a NAND gate, when A=0, the output must be 1. A 0 input locks the NAND gate
  • When $\bar{S}=0$ then $Q$ will be 1 no matter what!
  • When $\bar{R}=0$ then $\bar{Q}$ will be 1 no matter what!

However, in the case where $\bar{S}$ and $\bar{R}$ are 0, the $Q_R$ and $Q_{T+1}$ haven’t really settled on a value. The output becomes 1, 1, which is forbidden because it makes no sense.

• When $\bar{S}=\bar{R}=0$, this is a forbidden state

Essentially with S = R = 1, that is your forbidden state for any latch. Also, $S=R=0$ implies no change happens; things hold their data

Race Condition

Going from 00 to 11 results in a race condition where whichever input is “inputted” first decides which of the last 2 rows in the chart given does the output assume.

• Whichever gets received first depends on gate delays and RNG

SR Latch

• R and S retain their meaning clearer. Also S=R=1 is a forbidden state.
• We have unstable behaviour when going from 11 to 00
• Otherwise similar to the other latch