Convert a binary number, represented as a string (e.g. '101010'), to its decimal equivalent using first principles.
Implement binary to decimal conversion. Given a binary input string, your program should produce a decimal output. The program should handle invalid inputs.
Decimal is a base-10 system.
A number 23 in base 10 notation can be understood as a linear combination of powers of 10:
23 => 2*10^1 + 3*10^0 => 2*10 + 3*1 = 23 base 10
Binary is similar, but uses powers of 2 rather than powers of 10.
101 => 1*2^2 + 0*2^1 + 1*2^0 => 1*4 + 0*2 + 1*1 => 4 + 1 => 5 base 10.
All of Computer Science http://www.wolframalpha.com/input/?i=binary&a=*C.binary-_*MathWorld-
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
# # Test binary_convert with some examples # # s0 - num of tests left to run # s1 - address of input word # s2 - address of expected output word # s3 - char byte # s4 - output word # # binary_convert must: # - be named binary_convert and declared as global # - read input address of string from a0 # - follow the convention of using the t0-9 registers for temporary storage # - (if it uses s0-7 then it is responsible for pushing existing values to the stack then popping them back off before returning) # - write integer result to v0 .data # number of test cases n: .word 9 # input values (null terminated) & expected output values (word sized ints) ins: .asciiz "0", "1", "10", "11", "100", "1001", "11010", "10001101000", "000011111" outs: .word 0, 1, 2, 3, 4, 9, 26, 1128, 31 failmsg: .asciiz "failed for test input: " okmsg: .asciiz "all tests passed" .text runner: lw $s0, n la $s1, ins la $s2, outs run_test: move $a0, $s1 # move address of input str to a0 jal binary_convert # call subroutine under test move $v1, $v0 # move return value in v0 to v1 because we need v0 for syscall lw $s4, 0($s2) # read expected output from memory bne $v1, $s4, exit_fail # if expected doesn't match actual, jump to fail scan: addi $s1, $s1, 1 # move input address on byte forward lb $s3, 0($s1) # load byte beq $s3, $zero, done_scan # if char null, break loop j scan # loop done_scan: addi $s1, $s1, 1 # move input address on byte past null addi $s2, $s2, 4 # move to next word in output sub $s0, $s0, 1 # decrement num of tests left to run bgt $s0, $zero, run_test # if more than zero tests to run, jump to run_test exit_ok: la $a0, okmsg # put address of okmsg into a0 li $v0, 4 # 4 is print string syscall li $v0, 10 # 10 is exit with zero status (clean exit) syscall exit_fail: la $a0, failmsg # put address of failmsg into a0 li $v0, 4 # 4 is print string syscall move $a0, $s1 # print input that failed on li $v0, 4 syscall li $a0, 1 # set error code to 1 li $v0, 17 # 17 is exit with error syscall # # Include your implementation here if you wish to run this from the MARS GUI. # .include "impl.mips"
.globl binary_convert # input is a0, output is v0 # $t1 is the current char binary_convert: li $v0, 0 #reset the acc LOOP: lb $t1, 0($a0) beqz $t1, STOP #stop on \0 subi $t1, $t1, '0' #ascii offset '0' -> 0, '1' -> 1 sll $v0, $v0, 1 #shift the binary or $v0, $v0, $t1 #set the new bit addi $a0, $a0, 1 #pointer incr j LOOP STOP: jr $ra #return (program exits without this)
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