C D. A B D. D E E' A' B' C' CLK (a) Four-stage switch-tail ring counter Flip-flop outputs Sequence number AND gate required for output A B E A'E' AB' 1 1 1 BC' 1 1 1 CE' 1 1 1 1 1 AE 1 1 1 0 0 A'B 1 B'C СЕ (b) Count sequence and required decoding FIGURE 6.18

4. Design a logic circuit to compare 1-bit binary numbers, using NAND gates only.

A hidden passage is controlled by a redstone circuit for an adder which performs binary addition two bits at a time. He notes that it adds the inputs (x2i, y21) and (x2i+1, Y2i-1), the (2i)th and (2i+1)th bits of two binary numbers, and returns the sum as outputs s2i, S2+1. The addition is performed each clock cycle, starting from i = 0 until i = п 1, where n is the number of bits and 2 presumed to be even. For example, when adding x = 011010, and y number as x1:0 and y1:0 respectively. In this case, X1:0 is 10 and y1:0 = 01, and the carry bit co is 1. Our sum, s,0 is 00 and the next carry bit c, is 1. On the next clock cycle, we look at the next two 0110012, we take the first two bits of each bits, X3:2 = 10 and y3:2 = 10, so our sum s3-2 is 01, but we have a carry c4 1. Finally, our last addition to perform is on X5-4 = 01 and y5:4 = 01, with a carry bit c4 = 1. Our sum therefore is s54 = 11 with carry C6 = 0. Our final result of the addition is 1101002. You are only responsible for…

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