This problem involves the design of a circuit that finds the square root of an 8-bit unsigned binary number N using the method of subtracting out odd integers. To find the square root of N, we subtract 1, then 3, then 5, and so on, until we can no longer subtract without the result going negative. The number of times we subtract is equal to the square root of N. For example, to find √27 : 27 - 1 = 26; 26 - 3 = 23; 23 - 5 = 18; 18 - 7 = 11; 11 - 9 = 2; 2 - 11 (can’t subtract). Since we subtracted five times, √27 = 5. The final odd integer is 11₁₀ = 1011₂, and this consists of the square root (101₂ = 5₁₀) followed by a 1.
(a) Draw a block diagram of the square rooter that includes a register to hold N, a subtracter, a register to hold the odd integers, and a control circuit. Indicate where to read the final square root. Define the control signals used on the diagram.
(b) Draw a state graph for the control circuit using a minimum number of states. The N register should be loaded when St = 1. When the square root is complete, the control circuit should output a done signal and wait until St = 0 before resetting.